The cutoff wavelengths of elliptical waveguides are calculated by using a meshless collocation method with the radial basis functions, which only needs point sampling, and no mesh discretization is performed. The field value at any point inside the waveguide can be obtained by interpolation using the Wendland radial basis functions, which have been proven effective in scattered data interpolation. The Hermite interpolation is used to give a more accurate approximation of the first‐order derivatives. The accuracy and robustness of the proposed method are validated by numerical examples. Due to the advantage that no special consideration of the contour is needed, the method can also be applied to waveguides with arbitrary cross sections. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 162–165, 2002.