For the reader's reference, this is the Alamo at the time of the siege: https://i0.wp.com/www.latinamericanstudies.org/maps/alamo-map-3.gif
The Alamo is a mid-18th century Franciscan mission that became a garrison for Spanish and then Mexican cavalry units before ultimately being fortified by, and then captured from, Mexican general Perfecto de Cos in the 1835 Siege of Bexar. The main compound is a rough rectangle, slightly wider on the northern side, about 537 feet by 244 feet, with a total perimeter of just under 1500 feet; the church and palisade add a bit more. The walls are mainly adobe, but the crumbling north wall has been reinforced with rammed earth, a palisade has been erected between the southeast wall and the church, and a strong earthwork lunette has been thrown up outside the main gate, in the south wall. The fortification is almost wholly surrounded by the acequia (irrigation ditch), but these are shallow barriers. Being South Texas in early spring, there is little cover or concealment outside the walls, save for some small shacks which the defenders will eventually burn.
As for the garrison? The reasonable estimates for the Alamo's strength at any one time during the siege vary between 180 and 250 men. Some are regulars, but the majority of the Texians are volunteers. With the exception of their officers, most are newcomers to Texas and missed the previous year's fight at Bexar. Their commanders, William Barret Travis and James Bowie, are veterans of at least one campaign, though Bowie would soon be removed from active command by a strange malady. They have been poorly supplied by the Texian provisional government, want for warm clothing, and the fortification is not provisioned to withstand a lengthy siege. Despite that, they are at least well armed, even if the powder is short. There are 21 cannon in the compound, but only 18 of them are mounted and will play a role. Of these, only three are 12-pounders or larger. The largest, an 18-pounder, is sited on the southwest corner where it can cover the town of Bexar. Lighter guns are distributed throughout the perimeter. In addition to cannon, the garrison is well supplied with Mexican muskets captured after the Siege of Bexar.
Now, I've just given you a probably overly lengthy description of the Alamo's military situation on the eve of the siege. Here's what it means. The Alamo represents a significant obstacle for any force that lacks a siege train. The garrison is too small to fully defend the oversized perimeter, but they have enough cannon and enough small arms (two or three spare muskets per man) to turn any kind of an improvised infantry attack into a gory debacle. For an army with artillery, sappers, and experience in using them, it is a much less daunting task. It is an improvised fortification, and it shows. The walls were not built to stand up to cannon fire and have a vulnerable dead zone at their base. Most of the Texian cannon lack the range, and all lack the powder, to engage in an extensive artillery duel with Mexican batteries.
What followed is almost a cliche of early 19th century siege warfare. The arriving Mexican vanguard isolated the garrison and demanded surrender - and were refused. When the garrison awoke, they found a fortified battery 400 yards west of the fort. As the cannon began to pound the fort, Santa Anna reconnoitered. On the third day, the Mexicans made a small, battalion-sized attack on the west wall of the Alamo. The attack seems not to have been in earnest, and the Texians beat it off with relative ease. While they were dealing with the infantry probe, however, the Mexicans established new field works around the Alamo. On the fifth day, the Mexicans dammed the acequia and cut off the defenders' main source of water, while simultaneously building a new, closer trench line to the south. All the time, more guns continued to arrive and join in the cannonade.
By the 11th day of the siege, the Mexican batteries were only 200 yards from the walls, and while the guns bashed away at them, howitzers threw explosive shell into the compound. The bombardment inflicted few casualties, but it battered the defense, and the defenders. Men who had been kept from sleep by shelling, guard duty, and patrols, who were short on food and water, were then required to repair crumbling walls and dig ditches. Every day made them weaker. On the 12th day, the Mexicans began final preparations for an assault the following morning.
The assault itself was a brief, bloody denouement. 1,000-1,200 or so Mexican soldiers (rising to more than 1,500 once reserves were thrown in) advanced on the Alamo from three directions in the predawn hours. They silenced the outposts beyond the walls, but seem to have given themselves away by a spontaneous cheer. Despite that lapse, they were almost to the walls by the time the Texians could turn out to meet them. The Texians began firing their cannon blindly into the dark. Loaded with canister and grapeshot, they functioned as enormous shotguns, tearing great holes in Mexican ranks from point blank range. But though they could maul the oncoming columns, they could not stop them, and the Mexican soldiers broke through along several points, first in the north, then in the southwest, and the assault became a snake hunt, with onrushing Mexicans chasing broken Texians through the fort. Some Texians may have tried to break out from the Alamo and been cut down by the Mexican cavalry; a few may have been captured. But most died at the walls or in the terrified aftermath of their breaching. Mexican casualties are debatable, but somewhere between 400 and 600 is probably safe; the assault force was victorious, but thoroughly busted up. If anything, the Mexicans probably didn't soften up the defenses enough, but generals do not have an infinite amount of time available to them, and the result is that men bleed for it. Santa Anna literally could not afford a long campaign; the government had gone extensively into debt to finance this effort at reconquest and it had to be done quick and on the cheap.
There's also a strategic reason for the Alamo dragging on as long as it did. Santa Anna may have been trying to lure Texian reinforcements to the Alamo so that they could be destroyed by his army while still on the march. Even if this was not his intention, he was certainly aware of the possibility, and took measures to counter any such relief attempt.
