A numerical method using advanced nonlinear shear is used to study the thermal vibration of functionally graded material (FGM) thick circular cylindrical shells. The third-order shear deformation theory (TSDT) of displacements is applied and the equations are derived of the motion of cylindrical shells and the expression of the advanced nonlinear varied shear factor. The expressions of stiffness of thick composited two-layer FGM circular cylindrical shells with sinusoidal rising temperature are applied. The partial differential equation (PDE) in dynamic equilibrium of thick FGM circular cylindrical shells is derived with respect to shear rotations and displacements under terms of thermal–mechanical loads and density inertia terms. Important parametric effects of the advanced nonlinear varied shear factor, power law index, and temperature on the stress and displacement of thick FGM circular cylindrical shells are studied. Additionally, the advanced nonlinear varied shear factor effect is included and studied for a vibrating frequency using a fully homogeneous equation.