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Based on the reproducing kernel particle method (RKPM) and the radial basis function (RBF), the radial basis reproducing kernel particle method (RRKPM) is presented for solving geometrically nonlinear problems. The advantages of the presented method are that it can eliminate the negative effect of diverse kernel functions on the computational accuracy and has greater computational accuracy and better convergence than the RKPM. Using the weak form of Galerkin integration and the Total Lagrangian (T.L.) formulation, the correlation formulae of the RRKPM for geometrically nonlinear problem are obtained. Newton–Raphson (N-R) iterative method is utilized in the process of numerical solution. Moreover, penalty factor, the scaling parameter, the shaped parameter of the RBF and loading step number are discussed. To prove validity of the proposed method, several numerical examples are simulated and compared to finite element method (FEM) solutions.