Abstract: Manifold Method (MM) developed by Dr. Shi is a noel and very versatile numerical method. which is applicable to both continuous deformation problems and discontinuous deformation problems in structural and geotechnical engineering in a unified framework. In this paper, the generalized mathematical formulations of the manifold method using polynomial cover functions with high orders are presented. Accordingly, the manifold method using the second-order polynomial cover functions is given in detail. Afterwards, the Visual C++ computer programs of the MM using the second and first-order polynomial cover functions have been developed respectively, and applied to the analysis of a purely-bending beam subjected to bending moment. The calculated results with use of the 2nd-order MM agree fairly Well with theoretical solutions. However, the results computed for the same model using the 1st-Order MM have marked deviation ho the theoretical values. The comparison between the calculated results for this numerical example indicates that the computational accuracy of the MM can be greatly improved if a higher order cover function is employed. Therefore, it is practically necessary and important to develop a higher order manifold method for complicated deformation problems.