Multidimensional elastostatic problems can be solved by a collocation method using radial basis function. This meshfree point collocation method has some advantages: it dose not require special treatment for essential boundary condition nor the time-consuming integration of a weak form. Neither the connectivity of the mesh nor differentiability of the weight function is necessary. In this paper a meshfree algorithm based on radial basis function is proposed and applied to the analysis of typical two-dimensional elastostatic problems. The main advantage of such 2D meshfree approach is its simplicity in both formulation and implementation. The basic characteristic of the formulation is the definition of a global approximation for the variables of interest from a set of radial basis functions conveniently placed at the boundary and in the domain. Generalized multiquadric radial basis function is considered as interpolation function in this method. The performance and robustness are demonstrated by several numerical examples.