Abstract: Based on the research background of two dimensional elasticity problems, an idea of two-dimensional new fast multipole virtual boundary element collocation methods is proposed in this paper, in other words, a new fast multipole method (FMM) and the generalized minimal residual (GMRES) algorithm are jointly employed to solve the equations related to the virtual boundary element collocation method (VBEM). The numerical scheme suitable for original FMM with respect to two-dimensional problems of elasticity is optimized through introducing the concept of diagonalization in order to further improve the efficiency of the problem to be solved. Then large-scale numerical simulations of elastostatics might be achieved by the method. Numerical examples have proved the feasibility, efficiency and calculating precision of the method. Moreover, this article idea has the generality and the extension in the engineering applications.