Abstract: A domain decomposition approach is proposed for solving the free and forced vibration of joined conical-cylindrical-conical shell (CCCS) structures with different boundary conditions. The CCCS is preliminarily divided into cylindrical and conical shell substructures along the locations of the junctions and the prescribed-displacement boundaries; then these shell substructures are further decomposed into smaller cylindrical and conical shell segments to accommodate the computing requirement of high-order vibration modes and responses. The constraint equations derived from all interface continuity conditions are incorporated into the system energy function by means of the subdomain generalized variational principle and the least-squares weighted residual method, which involves the reduction of conditional extremum problems to extremum problems without any constraints. Double mixed series, i.e. the Fourier series and Chebyshev orthogonal polynomials, are adopted as assumed admissible displacement functions for each shell segment. To test the convergence, efficiency and accuracy of the present method, free and forced vibration solutions for CCCSs with different boundary conditions are compared with those obtained using finite elment program ANSYS. Good agreement is observed and the present solution is found to be very efficient, robust and accurate.