The intent of the present study is to employ the extended Kantorovich method for semi-analytical solutions of laminated composite plates with arbitrary lamination and boundary conditions subjected to transverse loads. The method based on separation of spatial variables of displacement field components. Within the displacement field ofa first-order shear deformation theory, a laminated plate theory is developed. Using the principle of minimum total potential energy, two systems of coupled ordinary differential equations with constant coefficients are obtained. The equations are solved analytically by using the state-space approach. The results obtained are compared with the Levy-type solutions of cross-ply and antisymmetric angle-ply laminates with various admissible boundary conditions to verify the validity and accuracy of the present theory. Also, for other laminations and boundary conditions that there exist no Levy-type solutions the present results are compared with those obtained by other investigators and finite element method. It is found that the present results have very good agreements with those obtained by other methods.