At 17:21, the guy in this video, https://www.youtube.com/watch?v=5uwWlamONqs, who is supposed to be an expert in medieval armor, says that "Nobody ever used rectangular shields. That's ridiculous."
I've always seen pictures of roman soldiers with their big curved rectangular shields, and I didn't find anything in my brief googling to suggest that they didn't use them.
Is the guy in the video wrong or is everything in google wrong or is there something else happening here?
The Romans definitely did use rectangular shields. I have not seen the video, but this is not a subject that is in question. From a glance, the video is talking about the medieval period and probably does not mean to make a statement extending to the rest of history.
Here is a famous example of a 3rd century rectangular Roman scutum found at the fortress in Dura Europos
Here is a depication of a soldier with a rectangular scutum on the Tropeaum Trainani, the Adamklissi monument raised in celebration of Traian's Dacian wars. (Considered more accurate in its depiction than the Traian's more famous column in Rome.)
"by the beginning of the 1st century the vast majority of legionaries carried rectangular shields" - Goldsworthy, the Complete Roman Army (2003) p. 129
Not all Roman shields were rectangular. Some continued to carry shields with straight sides but rounded tops. There were also oval shields used. By late antiquity, the rectangular shields disappeared in favour of round or oval ones.
Furthermore, it should be noted (see both linked images) that although the shields were rectangular in outline, they were also sharply curved around the body. So they weren't flat rectangular boards. As Cassius Dio describes in his section on how to form the famous testudo formation:
The heavy-armed troops who use the oblong, curved, and cylindrical shields are drawn up around the outside, making a rectangular figure; and, facing outward and holding their arms at the ready, they enclose the rest. The others, who have flat shields, form a compact body in the centre and raise their shields over the heads of all the others, so that nothing but shields can be seen in every part of the phalanx alike and all the men by the density of the formation are under shelter from missiles. — Cassius Dio, Roman History book 49
So yes, Romans used rectangular curved shields. I am not aware of anyone calling this into question.
I think that Tobias Capwell's comment that "Nobody ever used rectangular shields. I mean, that's ridiculous. It's stupid" is meant only in the context of Anglo-Saxon/Viking warfare (in which nobody used rectangular shields), and the "ridiculous .. stupid" refers to using such shields in costuming for Anglo-Saxon/Viking times, rather than rectangular shields themselves being ridiculous or stupid.
While rectangular shields are less common than round and oval shields, they are far from rare.
Europe:
Pavises - large shields intended to sit on the ground rather than be held:
https://collections.royalarmouries.org/object/rac-object-520.html
https://www.metmuseum.org/art/collection/search/22858 - this one is huge: 171cm tall and 22kg(!!!)
https://www.metmuseum.org/art/collection/search/22857 - also huge; a few cm taller and about the same weight.
https://commons.wikimedia.org/wiki/File:Bohemian_-Archer%27s_Shield-_Walters_511371.jpg
Bucklers - small shields that cover little more than the hand:
Concave cavalry shields, which were often used in tournaments:
Other:
England, pre-Roman: https://www.britishmuseum.org/collection/object/H_1938-0507-157 - a metal miniature model of a shield
England, pre-Roman: https://www.britishmuseum.org/collection/object/H_1857-0715-1 - the well-known Battersea shield
Non-European:
Chad: https://www.britishmuseum.org/collection/object/E_Af1950-16-41
Sahara Desert: https://www.britishmuseum.org/collection/object/E_Af1990-11-1
Uganda: https://www.britishmuseum.org/collection/object/E_Af1913-276
Kenya: https://www.britishmuseum.org/collection/object/E_Af1947-16-94
Kenya: https://www.britishmuseum.org/collection/object/E_Af1938-0608-198
Tanzania: https://www.britishmuseum.org/collection/object/E_Af1919-76
Malawi: https://www.britishmuseum.org/collection/object/E_Af1927-0709-61
Mongolia: https://www.britishmuseum.org/collection/object/A_As-5239
Assam: https://www.britishmuseum.org/collection/object/A_As1986-Q-95
Assam (Naga): https://www.metmuseum.org/art/collection/search/31807
Assam (Naga): https://www.metmuseum.org/art/collection/search/31814
Nagaland: https://www.britishmuseum.org/collection/object/A_As1929-0415-57
Naga: https://www.britishmuseum.org/collection/object/A_As1917-1211-1
Burma: https://www.britishmuseum.org/collection/object/A_As-7857
Burma: https://www.britishmuseum.org/collection/object/A_As-7856
Burma: https://www.britishmuseum.org/collection/object/A_As1986-22-161
Philippines (Igorot): https://www.britishmuseum.org/collection/object/A_As1914-0414-68
Philippines (Bagobo): https://www.metmuseum.org/art/collection/search/31809
Borneo: https://www.britishmuseum.org/collection/object/A_As1900-637
Borneo: https://www.britishmuseum.org/collection/object/A_As1904-0416-92
Borneo: https://www.britishmuseum.org/collection/object/A_As-234
Indonesia: https://www.britishmuseum.org/collection/object/A_As1891-0815-31
Indonesia: https://www.britishmuseum.org/collection/object/A_As1972-Q-3227
Indonesia(?): https://www.britishmuseum.org/collection/object/A_As1972-Q-999
Indonesia: https://www.britishmuseum.org/collection/object/A_As-5026
Indonesia: https://www.britishmuseum.org/collection/object/A_As-5661
Indonesia (Batak): https://www.britishmuseum.org/collection/object/A_As1895-0902-12
Indonesia: https://www.britishmuseum.org/collection/object/A_As1981-Q-18
Indonesia: https://www.britishmuseum.org/collection/object/A_As-7286 - very much like the Iron Age English model shield above
West Papua: https://www.britishmuseum.org/collection/object/E_Oc1982-02-9
Papua New Guinea (PNG): https://www.metmuseum.org/art/collection/search/311990
PNG: https://www.britishmuseum.org/collection/object/E_Oc1990-09-5 - decorated with modern paint
PNG: https://www.britishmuseum.org/collection/object/E_Oc1990-09-1 - again, modern paint; this time brighter
PNG: https://www.britishmuseum.org/collection/object/E_Oc1990-09-9 - modern paint, in a modern style
PNG: https://www.britishmuseum.org/collection/object/E_Oc1970-02-7
PNG: https://www.britishmuseum.org/collection/object/EA_Oc-F-T-6097 - showing the size of these often very large shields
PNG: https://www.britishmuseum.org/collection/object/EA_Oc-F-T-5537 - again, showing the size
PNG (New Britain): https://www.britishmuseum.org/collection/object/E_Oc1913-0524-15
Australia: https://www.britishmuseum.org/collection/object/E_Oc-1841_1
Australia: https://www.britishmuseum.org/collection/object/E_Oc1953-16-14
Rectangular shields have one big advantage over round shields: they can be tall without being as heavy (because they don't have to be as wide). Being rectangular rather than oval gives you a little more weight for the same thickness, and corners (either sharp or rounded), which can be either an advantage or disadvantage. Corners can stop a weapon from sliding around the side of the shield; this can be enhanced by making a shield with "horns" rather than just corners:
and
Corners can also make effective striking surfaces (shields can be used offensively as well as defensively). The disadvantage is that an opponent can sometimes use the corners to stop you from moving your shield, and you can bump yourself with them. One option is to make only one end of the shield flat, while having the other rounded. For example, the bottom of this shield might be rounded to stop bumping shins on the corner, or catching bottom corners in vegetation: