The structural analysis of orthotropic and linear elastic cross-ply laminated composite thick plates is made by considering complete effects of transverse shear and normal stresses. The solutions are obtained using the functional analysis method in conjunction with the Gateaux differential. A new functional with boundary condition terms is developed for the analysis. A four-node serendipity element with eight degrees of freedom is used. To ensure the accuracy of the developed mixed finite element (MFE), numerical results are compared with those of the published solutions. It has been proven that the developed MFE is highly accurate and efficient.