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In this paper, a structured grid based basis functions are used for global approximation in solution domain. A boundary region is selected to create relevant boundary trial and test functions. The B-Spline basis functions are used to approximate the boundary curves (surfaces in 3D) and describe the given boundary region. In this boundary region, boundary basis functions are constructed based on the same B-Spline basis functions for representing the boundary region and weight functions are created for modification of the global basis functions and the boundary basis functions. The modified basis functions maintain high order continuity and can at least reconstruct linear polynomial. Based on the modified basis functions, the solution is created to make the essential boundary conditions automatically satisfied. Meanwhile, the accuracy of the solution near the essential boundaries can be guaranteed. Furthermore, the solution also can be constructed to improve the accuracy of solution in the local region in which complex deformation exists. The present method has been used to solve some 2-D elasticity problems. The numerical results are compared with analytical and finite element analysis solutions to show that the method is stable and effective.