Compared to thick-walled situations, hoop stress is much more sensitive. A simplistic approach is to consider the casing as a thin-walled cylinder and the body as solid, then use the basic Lame equations for hoop stress:

σθ = pr/t

where p = radial interference pressure, r = mid-radius of the casing, t = wall thickness of the casing.

Interference determines p as follows: p = (δi/r) x (Es/(1−𝝂s2p); where δi = radial interference, Es = volumetric modulus of stainless steel, 𝝂s = Poisson’s ratio.

Axial stress is generally negligible for light loads, but the situation changes if you have long, thin casings with end constraints. The key point is high stress for thin wall = small interference. Prevent permanent ovalization by keeping hoop stress from 304 stainless (yielding about 205 MPa) ~0.4-0.5·σ_y lower.