The stress-strain state of a pressurised spherical shell is studied by means of the exact 3D theory of elasticity and the 2D approximate shell theories of moderate thicknesses. The sphere is made of transversely isotropic material. The problem models the changes in the fluid pressure inside the human eye due to injected additional volume of liquid. The algebraic relationships for deflections and stresses are derived. 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. Analytical results found with the presented theories are compared with those obtained with FEM.