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For the analysis of Kirchhoff plate bending problems, a new meshless method is implemented. For the satisfaction of the C1 continuity condition in which the first derivative is treated an another primary variable, Hermite interpolation is enforced on standard reproducing kernel particle method. In order to impose essential boundary conditions on solving C1 continuity problems, shape function modifications are adopted. Through numerical tests, the characteristics and accuracy of the HRKPM are investigated and compared with the finite element analysis. By this implementation, it is shown that high accuracy is achieved by using HRKPM for solving Kirchhoff plate bending problems.