The algorithm idea of virtual boundary element collocation method with RBF interpolation on virtual boundary and diagonalization feature in fast multipole method is presented to study 2-D elasticity problems in this paper. In other words, the new fast multipole method (FMM) adopting diagonalization and the generalized minimal residual (GMRES) algorithm are jointly employed to solve the equations related to virtual boundary element collocation method (VBEM) with RBF interpolation on virtual boundary. In this paper, the numerical scheme suitable for original FMM with respect to two-dimensional problem of elasticity is optimized, through the introduction of concept of diagonalization, in terms of the radial basis function to express the unknown virtual load functions, 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 in the paper have proved the feasibility, efficiency and calculating precision of the method.