This study provides a parallel algorithm for meshfree analysis based on the radial point interpolation method. This algorithm is designed to suit graphics hardware that support compute unified device architecture, NVIDIA's software development environment on graphics processing units (GPUs). The radial point interpolation method is a meshfree method that enables strict imposition of Dirichlet boundary conditions, and it mainly consists of two steps: the process for assembly of the discrete linear system and the process for solving the linear system. This paper shows that both the processes can be performed effectively on the GPU by applying our parallel algorithm and at the same time, the costs for data transfer to and from the GPU can be reduced, because the processes related to the discrete linear system are performed independently on the GPU. Our numerical tests confirm that the algorithm performed on the GPU accelerates the computations by a factor of maximum 15.