[jcriddle4]

Material strength is really important. Atmospheric pressure is about 14 pounds per inch at sea level. You can probably drop that to 10 pounds per inch or maybe less. For a square foot of wall, at 10, you would be at 12 * 12 * 10 or 1440 pounds of pressure. So for the cylinder style of design a one foot high band say 30 feet in diameter would have over 40,000 pounds pushing on it. That design uses basalt fiber, which has been around for quite some time and is quite strong. https://en.wikipedia.org/wiki/Basalt_fiber

[elihu]

I think that's a good argument for building below grade. For instance, you dig a big hole, build a dome-like shell, bury it in dirt leaving a reinforced tunnel to the surface for a stairwell, then inflate a balloon inside the shell to provide an airtight living area. The weight of the ground counteracts the air pressure and it acts as a radiation shield.

(Alternatively, one could build the dome from the top down, excavating as you go.)

If dirt is about 80 pounds per square foot (I'll assume for the sake of argument that that's in the ballpark of the typical density of Martian sand), that's about 32 pounds in Mars gravity, or about 0.22 pounds per square inch per foot of depth. So, it would take about 45 feet of depth for the weight of the ground to match 10 psi of air pressure. Maybe that's a little too deep to be practical for a pure compressive structure, but maybe ten or twenty feet of depth can offset a significant amount of the tension even if the interior pressure is more than the weight of the ground on top.

I suppose you could also mound a pile of dirt on top over time.