In this study, the problems of shallow spherical shells on the Vlasov model and single-layer elastic foundations are investigated. The problems of axisymmetrical deformation of spherical shells on elastic single-layer foundations have also been considered. The external loads have been applied symmetrically relative to the shell centre. The differential equation of the shell has been solved according to the Bessel and Hankel functions, then constants of integration have been calculated from boundary and continuity conditions. This method has been applied to the analysis of the bottoms of cylindrical reservoirs. For the effect of the cylindrical reservoir walls on the strains of the bottom the method of flexibility has been used. Some of the results from the Vlasov model have been compared to the Winkler model and elastic half-space.