Abstract: A semi-analytical method-modified Fourier series is proposed to solve the free vibration of the coupled conical-cylindrical-spherical shell with closed ends.Based on energy function,the classical thin plate theory and Love shell theory are combined toconstruct the theoretical model of the coupled conical-cylindrical-spherical shell.The natural frequencies of the coupled structurewith different cylindrical shel lengths,different semi angles of conical and spherical shell and different thicknesses of end plates arestudied.The displacement of each substructure of the coupled shellis composed of the standard Fourier series and the auxiliary convergence functions.The introduction of the auxiliary functions can not only remove allthe potential discontinuities of traditionalFourier series at the connections,but also improve the convergence precision and speed of calculation.The research shows that thepresent method has good convergence,which the calculation results show a good agreement with the finite element method results.By analyzing the natural frequency,it is found that the changes of length,semi-angle and thickness of end plates have obvious influence on the free vibration of the conical-cylindrical-spherical shell.