In this study, ratcheting behavior of thick spherical vessels subjected to mechanical cyclic loads at elevated temperature, using the Chaboche unified viscoplastic model with combined kinematic and isotropic theory of plasticity, is investigated. Since this model is rate dependent, loading rate plays a crucial role on the ratcheting responses. A precise and general numerical procedure, using the modified successive approximation iterative method of solution to solve the non-linear equations, is developed to obtain the cyclic inelastic creep and plastic strains. Effects of loading and unloading rate, inside pressure, thickness of vessel, creep time and environmental temperature on ratcheting responses, and stress amplitude of the vessel due to the inside pressure cyclic loading at elevated temperature are obtained. The ratcheting response is observed for the load-controlled conditions, as investigated in this paper. It is shown that increasing the loading and unloading rates and the thickness of pressure vessels, result into decrease in the ratcheting rate while increasing the inside pressure, creep time, and temperature distribution increase the ratcheting rate. Also, stress amplitude decreases with increasing the creep time and thickness of vessel. On the other hand, increasing the loading and unloading rate, inside pressure, and temperature distribution result into increasing the stress amplitude. The results obtained using the applied method in this study is verified with the experimental data given in the literature. By simplifying the constitutive model, numerical results are compared with the finite elements results.