Per TO&E 7-17 of 1 February 1940, the U.S. rifle squad was organized as follows;

1 February 1940:

Quantity	SSN	Rank	Role
1r	745	Sergeant	Squad leader
1gs	745	Corporal	Squad leader, assistant
10r	745	Pvt./Pfc.	Rifleman

• g: armed with launcher, grenade, Mk. IV

• r: armed with rifle, U.S., cal. .30, M1

• s: armed with rifle, U.S., cal. .30, M1903/A1

Equipment	Quantity
Launcher, grenade, Mk. IV	1
Rifle, U.S., cal. .30, M1	11
Rifle, U.S., cal. 30, M1903/A1	1

On paper, all men were to be armed with the new M1 Garand semi-automatic rifle. As the Garand was still replacing the M1903 Springfield at this time, this was not always the case. A suitable grenade launching attachment for the M1 rifle had yet to be developed, so U.S. versions of French-made grenade launchers from World War I, (the Mk. IV) and later M1 grenade launchers for use with an M1903 rifle were issued to each squad, for use by the assistant squad leader. You will notice the absence of the Browning Automatic Rifle. Until October 1940 each platoon, on paper, had four squads, three rifle and one "automatic weapons" squad with two BARs. The automatic weapons squad was deleted with the 1 October 1940 revision of TO&E 7-17, although the BAR was not returned yet.

1 October 1940:

Quantity	SSN	Rank	Role
1r	745	Sergeant	Squad leader
1gs	745	Corporal	Squad leader, assistant
10r	745	Pvt./Pfc.	Rifleman

• g: armed with launcher, grenade, Mk. IV

• r: armed with rifle, U.S., cal. .30, M1

• s: armed with rifle, U.S., cal. .30, M1903/A1

Equipment	Quantity
Launcher, grenade, Mk. IV	1
Rifle, U.S., cal. .30, M1	11
Rifle, U.S., cal. 30, M1903/A1	1

On 1 March 1943, the BAR was returned to the rifle squad. The M1 grenade launcher for use with the M1903 Springfield rifle had been standardized on September 9, 1941, and was issued to replace the obsolete Mk. IV. A suitable grenade launcher for the M1 Garand, the M7, was still in development, so the M1903 rifle was kept in the squad to provide a grenade-launching capability.

The M7 grenade launcher was standardized on February 11, 1943, and began production in July, but it would not begin to reach frontline troops in significant numbers until a year later. To ease the shortage of M7 grenade launchers, eliminate M1903 rifles from squads, and replace the dangerous (the arming pin could unknowingly become snagged and fall out, resulting in the user carrying around a live grenade) M17 fragmentation rifle grenade, the M1 Grenade Projection Adapter was standardized as an alternative. This one-time-use device, a set of fins with a short shaft and three "claws," allowed a standard Mk II fragmentation grenade to be fired from an M1 rifle.

1 March 1943:

Quantity	SSN	Rank	Role
1r	745	Sergeant	Squad leader
1gs	745	Corporal	Squad leader, assistant
7r	745	Pvt./Pfc.	Rifleman
1b	746	Pvt./Pfc.	Rifleman, automatic
1r	746	Pvt./Pfc.	Rifleman, automatic, assistant
1r	746	Pvt./Pfc.	Ammunition bearer

• b: armed with rifle, automatic, cal. .30

• g: armed with launcher, grenade, M1

• r: armed with rifle, U.S., cal. .30, M1

• s: armed with rifle, U.S., cal. .30, M1903A3

Equipment	Quantity
Launcher, grenade, M1	1
Rifle, Browning, automatic, cal. .30, M1918A2	1
Rifle, U.S., cal. .30, M1	11
Rifle, U.S., cal. 30, M1903A3	1

In practice, the BAR, as it was not a true light machine gun, was often used as a one-man weapon. Many users removed the bipod and used it as a kind of battle rifle. With Change 1 of 30 June 1944, six BARs and six M3 submachine guns were issued unallocated to each rifle company headquarters, to be distributed as the company commander saw fit. With the 26 February 1944 revision of TO&E 7-17, squad leaders and their assistants were promoted to Staff Sergeant and Sergeant, respectively. The M7 grenade launcher was beginning to enter widespread use, and was issued three to each rifle squad; with the introduction of the M1 Grenade Projection Adapter, the M7 was mostly used to fire HEAT or smoke grenades.

26 February 1944:

Quantity	SSN	Rank	Role
1r	745	Staff Sergeant	Squad leader
1gr	745	Sergeant	Squad leader, assistant
7r(2gr)	745	Pvt./Pfc.	Rifleman
1b	746	Pvt./Pfc.	Rifleman, automatic
1r	746	Pvt./Pfc.	Rifleman, automatic, assistant
1r	746	Pvt./Pfc.	Ammunition bearer

• b: armed with rifle, automatic, cal. .30

• g: armed with launcher, grenade, M7

• r: armed with rifle, U.S., cal. .30, M1

Equipment	Quantity
Launcher, grenade, M7	3
Rifle, Browning, automatic, cal. .30, M1918A2	1
Rifle, U.S., cal. .30, M1	11

Sources:

U.S. Infantry Weapons of World War II, by Bruce N. Canfield

U.S. rifle grenades

TO&E 7-17 Infantry Rifle Company, dated 1 February 1940

TO&E 7-17 Infantry Rifle Company, dated 1 October 1940

TO&E 7-17 Infantry Rifle Company, dated 1 March 1943

TO&E 7-17 Infantry Rifle Company, dated 26 February 1944

In the Red Army, TO&E 04/401 issued on April 5th, 1941, defined an infantry squad as 11 men:

• Junior Sergeant or Sergeant (commander) with SVT-40

• Machinegunner armed with a DP machinegun and an assistant

• Two submachinegunners with PPD-40 submachineguns

• Six riflemen with SVT-40s.

TO&E 04/551 issued on December 1942 changed the structure to a commander, a commander's assistant (both sergeants of some rank), 7 riflemen, 1 submachinegunner, and one or two light machineguns (2 types of each squad in a rifle platoon).

On August 22nd, 1943, TO&E 04/550 reduced a platoon to three infantry squads, and changed the composition to one sergeant, one machinegun, and ten riflemen.

It is not included in the question, but as an comparison, I can offer how a Swedish rifle squad looked.

1939 (12 men).

Role	Number	Weapon
Squad leader	1	Rifle
Assistant squad leader	1	Rifle
LMG man	1	LMG
Rifleman	9	Rifle

There's SMGs available at the regimental HQ for special missions. In 1939 6 per battalion, but the number quickly grew, and by mid-1940 or so each squad leader would be equipped with an SMG instead of a rifle.

Riflemen carried 40 shots for their own rifle and two magazines for the squad LMG (20 shots each, for a total of 40 shots). Men with SMG carried 4 filled magazines for 200 shots while the LMG man carried 12 magazines for a total of 240 shots.

1941 (10 men).

Role	Number	Weapon
Squad leader	1	SMG
Assistant squad leader	1	Rifle
LMG man	1	LMG
Assistant LMG man	1	Rifle
Rifleman	6	Rifle

The assistant LMG man carried the ammunition not carried by the squad leader and spare barrels for the LMG.

1943 (10 men).

Role	Number	Weapon
Squad leader	1	SMG
Assistant squad leader	1	SMG
LMG man	1	LMG
Assistant LMG man	1	Rifle
Sharpshooter	1	Scoped rifle
Rifleman	2	Semi-automatic rifle
Rifleman	3	Rifle

While the organisaion called for 2 men with semi-automatic rifles, the teething problems of the 6,5x55mm AG m/42 meant that one of them usually carried a regular file until late 1944.

Weapons used.

SMGs are usually 9x19mm K-pist m/37-39, a license-produced shortened version of the Finnish Suomi K/31 Lahti SMG, using a 50-shot coffin double rof straight magazine. Early war there were purchases of German MP 34 (1 800) and US Thompsons (500), but these were quickly sent to local defence units.

Rifles were usually the long 6,5x55mm Gevär m/96 (Mauser 1896) bolt-action rifle, but later in the war shortened 6,5x55mm Gevär m/38 with turned down bolt handles became more common.

Scoped rifles were 6,5x55mm Gevär m/41, which were Gevär m/96 chosen for their accuracy and mounted with a 6x scope of German origin.

Semi-automatic rifles were the 6,5x55mm AG m/42, which suffered teething problems and were not available in numbers until late 1943.

LMGs are usually 6,5x55mm Kg m/37, a license-produced Browning BAR with FN modifications (quickly interchangable barrel with a handle, bipod and pistol grip), but the older 6,5x55mm Kg m/21 (earlier version of the BAR without the interchangable barrel) was common early in the war. The 7,92x57mm Kg m/39 (ex-Czechoslovak ZB-26 purchased from Germany) and the 6,5x55mm Kg m/40 (German Knorr-Bremse MG 35/36) were also available, but also quickly relegated to local defence units.

Just in general or regarding a specific time period? Early war, mid-war, late war, etc...?