A new version of the method of approximate particular solutions using radial basis functions has been proposed for solving a general class of elliptic partial differential equations. In the solution process, the Laplacian is kept on the left-hand side as a main differential operator. The other terms are moved to the right-hand side and treated as part of the forcing term. In this way the close-form particular solution is easy to obtain using various radial basis functions. The numerical scheme

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... f the new method of approximate particular solutions is simple to implement and yet very accurate. Three numerical examples are given and the results are compared to Kansa's method and the method of fundamental solutions.