Abstract: The laminated composite cone-cylindrical connected shell under internal pressure is analysed by the use of finite element displacement method based on laminated anisotropic shell theory. The numerical calculations are performed by using a computer program DDJTTQ-3, which was developed from the general purpose program DDJ-W for composed structure analysis¹. The conecylidrical connected shell is modeled by using triangular laminated composite shell elements on the base of discrete Kirchhoff's hypothesis and taking coupling effect into consideration.The expression of foregoing element stiffness matrix is given in the rapar.Two numerical examples are presented for both isotropic and laminated composite cone-cylindrical shell junction.The numerical results show that the computational results in this paper agree well with those from 3-D and axisymmetric curve finite element methods, which proves that the triangular laminated composite shell element is quite accurate.The displacement variation along the shell is strongly dependent on the elastic behaviour and ply numbers of composite materials.