This paper examines the idea that reversible hysteresis in MAX phases is caused by the formation, growth and collapse of unstable, or incipient, kink bands. In situ X-ray diffraction of polycrystalline Ti3SiC2 in compression showed that residual elastic lattice strains developed during the first loading cycle and remained approximately constant afterwards. These residual strains were compressive in grains with a low Schmid factor and tensile in grains with a high Schmid factor, consistent with previous observations of plastically deformed hexagonal metals. In contrast, incipient kink bands would be expected to collapse completely, without any residual strain. Elastoplastic self-consistent simulations showed that reversible hysteresis is predicted if some grains yield by slip on the basal plane, while others remain predominantly elastic, giving both the experimentally observed magnitude of the work dissipated and its dependence on the maximum applied stress. The reversible hysteresis in single crystals was studied by cyclically indenting thin films of Ti3SiC2 and Ti3SiC2/TiC multilayers on Al2O3 substrates. The work dissipated in the multilayer films was greater than in Ti3SiC2 alone, despite the reduction in volume fraction of Ti3SiC2. Reversible hysteresis was also observed during indentation of single-crystal cubic MgO, demonstrating that this behaviour can occur if there are insufficient slip systems to accommodate the strain around the indentation. These results show that reversible hysteresis is associated with conventional dislocation flow, without the need for unstable kinking.