In this paper, a double walled cylindrical shell model based on Donnell shell theory and strain gradient theory is constructed. The van der Waals (vdWs) interactive forces between adjacent layers are depicted as sets of linear springs. An energy equation for double layered shell model considering vdWs interactive between layers is presented. A moving Kriging interpolation-based meshfree method is utilized to obtain the analytical solutions for the cylindrical shell. The C² continuum shape function is constructed via the moving Kriging interpolation which satisfies the unbiasedness and minimum variance. The convergence and accuracy of the present method is validated. The effect of small-scale parameters, boundary conditions and the length-to-radius on the frequencies are carried out and some anti-phase mode shapes are obtained. Meanwhile, it is concluded that the mesh-free moving Kriging interpolation method has high precision and good stability in dealing with higher-order partial differential equations.