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We propose a systematic approach to accurate imposition of material interface conditions for the meshless radial point interpolation method (RPIM). A new set of equations for updating fields at interfaces is derived. A piecewise polynomial and a modified radial basis function are proposed and applied to account for field discontinuities near the interfaces. In contrast to the previous work, the proposed approach incorporates material properties and reduces geometrical dependence of the interpolation function. Numerical results show that the proposed approach significantly improves the simulation accuracy of the RPIM at a cost of a small overhead in computational time.