For the mechanical analyses of the axisymmetric structures in civil and mechanical engineering, combining the interpolating reproducing kernel particle method and the principle of minimum potential energy of space axisymmetrical elastic problems, the interpolating particle method for space axisymmetrical problem of elasticty is presented. And the corresponding matrix equations are deduced. This method employs the shape function with interpolating properties of scatter points and forms the displacement trial function to get rid of dependence on meshes, so it has an advantage that it can directly exert boundary conditions and can increase the computation efficiency. This method can obtain the global continuous stress field directly and avoid the fitting calculation error of stress in the post-processing of finite element method, then it is a high-precision numerical simulation method. Numerical examples are given to show the validity of the new mesh-less method in the paper.