In this study we have worked on the numerical solution of the multigroup neutron diffusion equation with the symmetric radial basis function collocation method. For the spatial approximation of the neutron flux, multiquadric, inverse multiquadric, and Gaussian basis functions are used as the interpolation functions. To test the performance of the method, both external and fission source problems are considered in two-dimensional Cartesian geometry. The effect of the shape parameter on the convergence and stability of the numerical algorithm is also investigated. The results have shown that, when the multiquadric is chosen, the symmetric RBF collocation method converges exponentially, and it is possible to obtain highly accurate multiplication factors and neutron flux distributions with this algorithm.