The method of global Fourier‐series approximation of the one‐electron energies ϵ(k) in the Brillouin zone is considered. To calculate the Fourier series expansions of the ϵ(k)‐functions optimal for trigonometric polynomials theoretical‐numerical nets are used. Convergence and accuracy of the approximation is investigated using one‐ and two‐band models of the ϵ(k)‐dependence. It is shown that the method described is more accurate then piecewise linear interpolation in the volumes of elementary tetrahedra, generated in regular nets, and is comparable to piecewise quadratic interpolation.