Based on the three-dimensional elasticity theory，the smooth stochastic response model of three-dimensional sandwiched cylindrical shells is established by using the unified series method and the pseudo-excitation method （PEM）. The cylindrical shell subdomains are divided according to the interlayer property differences of the sandwich material，and the kinetic energy，strain energy，boundary potential energy and smooth random excitation work of each subdomain are established by using three-dimensional elasticity theory combined with the virtual excitation method. The mechanical coordination conditions between the layered subdomains are converted into coupling condition energies by the coupling penalty function method，and then the overall energy generalization of the sandwiched cylindrical shell is obtained by superposing the energies of each subdomain. The displacement components of each subdomain are constructed using a unified level expression and solved by combining the Rayleigh-Ritz method to obtain the stochastic response of the three-dimensional sandwiched cylindrical shell structure. The correctness of the stochastic response model is verified by comparison with literature and finite element results. Finally，the effects of thickness-to-radius ratio，lay-up angle of laminated-functional gradient sandwich material and power-law index on the random response of three-dimensional sandwiched cylindrical shell are analyzed.