A general procedure is presented for the nonlinear analysis of the forced response of structural elements to harmonic excitations. Internal resonances (i.e., modal interactions) are taken into account. All excitations are considered, with special consideration given to resonant excitations. The general procedure is applied to clamped‐hinged beams. The results reveal that exciting a higher mode may lead to a larger response in a lower interacting mode, contrary to the results of linear analyses.