The displacement trial function is reconstructed by reproducing kernel particle shape function method with interpolation property on discrete points, then combining the principle of minimum potential energy of elasticity, the new interpolating reproducing kernel particle method to analyze the plane problem of elasticity is obtained. Because interpolation reproducing kernel particle shape function has a point interpolation property and no less than the high-order smoothness of kernel function, the difficulty for most of meshless methods to be used to deal with the essential boundary conditions is already overcome, and the high numerical accuracy is assured as well. Compared with the early meshless methods, this method has a high accuracy and a small scale of solving problem and it can be directly applied to boundary conditions. Numerical results for some typical examples of elasticity prove the proposed method to be valid.