Autofrettage process, adopted by the pressure vessel industry, enhances the static limit pressure of components. In addition, a significant increase in the fatigue life autofrettage components is also observed due to the inhibition of crack initiation and propagation. The application of autofrettage treated vessels can be extended to the power generation industry (fossil and nuclear), the petrochemical industry, the food industry (bacterial eradication container), and automotive applications (injection pump), among many others. In particular, spherical pressure vessels, due to their inherent stress and strain distributions require thinner walls compared to cylindrical vessels; therefore, they are extensively used in gas-cooled nuclear reactors, gas or liquid containers rather than heads of close-ended cylindrical vessels. In this paper analytical expressions have been derived for stress and strain during autofrettage process of spherical vessels with different material models. These formulas have been applied to evaluate the residual stresses, and optimized design in monotonic and cyclic loading conditions.