The exploration of the depths of the sea is an activity that is important for many branches of science; it is associated with the work of people and technology in extremely difficult external conditions, which, in their extremeness, are comparable, perhaps, only with the conquest of space. At the present stage, deep-sea surveys are carried out using various instruments, including manned ones. These machines do not belong to the class of military large-tonnage submarines, but to the so-called Bubble Subs. The hull, which is a translucent thick-walled spherical shell is the main characteristic feature of this type of underwater vehicle. The presented work lists the main problems faced by researchers in the strength analysis of such PMMA hulls. In particular, the issue of the significant difference between the results of calculations in cases where the material is considered as physically linear and as physically non-linear is disclosed in detail. In addition, the obtained numerical results are compared with the experimental data.