Abstarct: Abstract In this research, elastoplastic analysis of thick-walled truncated conical shells made of nonhomogenous FG materials with power-varying properties investigated by the use of shear deformation theory which is subjected to mechanical loads such as uniform internal pressure and rotation. The governing differential equations of the axially symmetric thick-walled cones made of FG materials have been obtained using the first and third-order shear deformation theories as well as the principle of virtual work. The obtained equations for the truncated cone with two clamped ends, which is a system of equations with variable coefficients, are solved with the help of the perturbation technique. The material state of the shell is elastic-perfectly plastic, and the Prandtl-Reuss flow rule has been used to express the behavior of the material in the plastic state, and the von Mises yield criterion has been used to determine the beginning of plasticization of the cone. The radial return mapping method has been used to obtain the stresses in the plastic state by returning the stress to the yield surface.The effect of parameters such as internal pressure, inhomogeneous constant of the FG cone, and angular velocity on the elasto-plastic solution of the cone has been investigated and compared with the results of finite element software. The results obtained for FGM rotating truncated pressurized conical vessles show that increasing the cone angle, the heterogeneity constant, and the angular velocity have significant effect on yielding. Elasto-plastic analysis of cylindrical and conical vessles can help designers to achieve optimal and cheaper design.