Calculations of spin-wave spectra in rare earth metals were carried out to find whether images of the electronic Fermi surface might be observable. In the space of spin-wave vectors q there should occur surfaces on which the frequencies have an infinite gradient with respect to q, the location of such abrupt changes, "kinks" in the dispersion curves, being determined by the shape of the Fermi surface. The spin-wave spectrum is found by assuming that the coupling between ionic spins takes place primarily through exchange scattering of conduction electrons, paralleling the calculation on the coupling of nuclear spins by Ruderman and Kittel. Spin-wave dispersion curves in two directions of high symmetry are computed numerically. The sought-for kinks in the dispersion curves are found to amount to about 2% of the maximum excitation frequency. The development is for ferromagnets, but extension to spiral antiferromagnets is taken up briefly.