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A local radial point interpolation method (LRPIM) based on local residual formulation ispresented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by theradial point interpolation method (PIM) and establishes discrete equations through a local residualformulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial functionand background mesh for integration is not necessary. Radial PIM is used for interpolation so thatsingularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by astraightforward and effective manner due to its Delta properties. Moreover, the approximation quality ofthe radial PIM is evaluated by the surface fitting of given functions. Numerical performance for thisLRPIM method is further studied through several numerical examples of solid mechanics.