In this work, we calculate the spin structure functions for spin-dependent elastic and inelastic WIMP scattering off 119Sn and 121Sb. Estimates for detection rates are also given. 119Sn and 121Sb are amenable to nuclear structure calculations using the nuclear shell model (NSM). With the possible exception of 201Hg, they are the only such nuclei still unexplored theoretically for their potential of inelastic WIMP scattering to a very low excited state. The present calculations were conducted using a state-of-the-art WIMP–nucleus scattering formalism, and the available effective NSM two-body interactions describe the spectroscopic properties of these nuclei reasonably well. Structure functions were found to be high for both nuclei in the case of elastic scattering. Elastic scattering dominated at the zero momentum transfer limit. Detection rate calculations indicated that inelastic scattering was relevant for both nuclei, even surpassing elastic rates for some recoil energies.