Abstract: Based on the authors earlier work entitled "A virtual boundary elementcollocation method for solvinhg problems of elasticity" published in the journal of Computational Structural Mechanics and its Applications, 8(1), 1991, in this paper the least square method is used to formulate the boundary integral equations satisfying the boundary conditons of the problem of elasticity and these integral equations are discretized by linear virtual boundary element. And then the analytical characteristics of these equations are studied. The Raita's (paИTa) criterion of error analysis is introduced for judgying the level of solution's error and an ideal effect is obtained. A VBELSM microcomputer programm is coded in which the Gaussion integral scheme is adopted and the symmetric conditions are considered to simplify calculation. The method can treat not only the smooth boundary but also the rough ones. The numerical examples show that this method has higher accuracy, the computer programm is reable and the algorithm is stable when the virtual boundary is selected suitably.