In this paper,a nonsingular boundary collocation scheme is constructed to solve the inverse problems in elasticity governed by the Navier equation.This method belongs to one kind of boundary-type meshless methods.It differs from the method of fundamental solutions,since the source point and collocation point can be both located on the real boundary at the same time.The purposed method uses the non-singular functions to substitute the fundamental solutions.As a result,it does not worry to face singular integral or calculate principal value,because there is no singularity when the source point and collocation point coincide together.The non-singular functions for the Navier equation is derived by using the H(o)rmander method.It is employed to solve the boundary value problems for verifying the feasibility and validity of solutions.Furthermore,we extend to deal with the inverse problem,or called Cauchy problem.Finally,several examples are employed to show the simplicity,efficiency and accuracy of the proposed approach.