This paper is concerned with the bending of laminated composite plates with arbitrary lay-up and general boundary conditions. The analysis is based on the small deflection, first-order shear deformation theory of composite plates, which utilizes the Reissner-Mindlin plate theory. In solving the aforementioned plate problems, a general algorithm based on the Ritz method and the use of beam orthogonal polynomials as coordinate functions is derived. This general algorithm provides an analytical approximate solution that can be applied to the static analysis of moderately thick laminated composite plates with any lamination scheme and combination of edge conditions. The convergence, accuracy, and flexibility of the obtained general algorithm are shown by computing several numerical examples and comparing some of them with results given in the literature. Some results, including general laminates and nonsymmetrical boundary conditions with free edges, are also presented.