In this paper a variation of the usual Vrefftz method is presented and applied to harmonic problems. Here, the fundamental solutions of the given problem are employed as expansion functions and their singularities are located outside the domain of the problem to avoid any handling of a singul-ar quantities. This method has a significant computationsal advantage in that here no integrations are required. Test problems have been analysed using tie proposed method and the results compared with those generated by the ReHlar Boundary Element Method using continuous and partially - dis-continous elements.