The unique superelastic properties of the Ni-Ti shape memory alloys (SMAs) have been found extensive practical application in many engineering fields, but the Ni-Ti SMAs exhibits elastic behavior in small load, so the elastic behavior of the Ni-Ti SMAs is studied by using meshless method of reproducing kernel particle method (RKPM) in this paper. The displacement boundary conditions are applied by utilizing the penalty function method, and the impact of penalty factor and parameter of influence domain on errors are discussed, and computational stability is analyzed. At last, the correctness of the RKPM in studying the elastic behavior of the Ni-Ti SMAs is evidenced by using three numerical examples.