The stress-strain state of a pressurized spherical shell and circular cylinder are studied by means of the exact 3D theory of elasticity and the 2D approximate shell theories of moderate thicknesses. Both the sphere and the cylinder are made of transversally isotropic material. The first problem models the changes in the fluid pressure inside the human eye due to injected additional volume of liquid. The pressurized cylinder is one of simplest model of the human vessels. The algebraic relationships for deflections and stresses are derived. Both described shell theories take into account the variation of the shell thickness, which can be important for soft materials, e.g. the human eye’s tissue. The asymptotical analysis of the exact 3D solutions has been performed and the accuracy of the approximate solutions, obtained with the approximate theories is analyzed. The effect of the thickness changes are also discussed.