In order to improve the accuracy in analyzing magneto-electro-elastic (MEE) structures, a stabilized node-based smoothed radial point interpolation method (SNS-RPIM) was proposed. Based on the traditional node-based smoothed radial point interpolation method, the stable item related to the gradient variance of the field variables was introduced to eliminate the uncertain parameter. The SNS-RPIM equations for multi-field coupling problems were derived, and the static responses of MEE structures were also solved. The results of SNS-RPIM were compared with those of finite element method. Numerical examples showed that SNS-RPIM can provide the result closer to the real solution and effectively solve the problem of 'overly-stiff' of finite element method. SNS-RPIM is better than FEM in terms of accuracy and convergence, which provides an effective analysis method for further application of MEE materials.