Abstract: In this paper, a generalized Kantorovich method based on cubic B-spline is presented for obtaining an approximate solution for the bending problem of arbitrary quadrilateral plates with various types of boundary conditions by the variational method and bilnear coordinate transformation. The spline generalized kantorovich method is a type of numerical kantorovich method, it not only can transfer two-dimension problems into one-dimension problems, also has the advantages the spline method possesses of, such as high precision, rapid convergence and suitability for various types of boundary conditions. Derived is a computional scheme well suited for various types of boundary conditions. The solutions of bending problem of the trapezoidal, parallelogram and rectangular plates are given as its particular cases. In comparison with the usual finite method, the main features of the present method are higher accuracy and more economy in computing storage and time requirements. This method has its generality and a good future.