The purpose of this work is to solve governing differential equations of laminated anisotropic plates and shells by using the Chebyshev collocation method. This method yields these results those can not be accomplished easily by both Navier¡¦s and Levy¡¦s methods in the case of any kind of stacking sequence in composite laminates with the variety of boundary conditions subjected to any type of loading. The Chebyshev polynomials have the characteristics of orthogonality and fast convergence. They and Gauss-Lobatto collocation points can be utilized to approximate the solution of these problems in this paper. Meanwhile, these results obtained by the method are presented as some mathematical functions that they are more applicable than some sets of data obtained by other methods. On the other hand, by simply mathematical transformation, it is easy to modify the range of Chebyshev polynomials from the interval [-1,1] into any intervals. In general, the research on laminated anisotropic plates is almost focused on the case of rectangular plate. It is difficult to handle the laminated anisotropic plate problems with the non-rectangular borders by traditional methods. However, through the merits of Chebyshev polynomials, such problems can be overcome as stated in this paper. Finally, some cases in the chapter of examples are illustrated to highlight the displacements, stress resultants and moment resultants of our proposed work. The preciseness is also found in comparison with numerical results by using finite element method incorporated with the software of NASTRAN.