SUMMARYIn this paper, the regularized meshless method (RMM) combined with the determinant rule is taken to analyze the cutoff wavelength of elliptical waveguide with arbitrary eccentricity. First, an improved desingularization technique of subtracting and adding back is introduced for RMM to discretize this problem. Then, the novel local minimum finding technique on the basis of Chebfun is applied to extract the cutoff wavelength from the determinant of the interpolation matrix of RMM. The numerical examples show that the RMM obtains consistent results with the conventional method of fundamental solutions but has advantage of well‐conditioning and no fictitious boundary. Our method provides another highly effective and stable candidate to solve the cutoff wavelength of elliptical waveguide. Copyright © 2012 John Wiley & Sons, Ltd.