Intromittent organs-structures that place gametes into a mate for internal fertilization-evolved many times within the animal kingdom, and are remarkable for their extravagant morphological diversity. Some taxa build intromittent organs from tissues with reproductive system antecedents, but others copulate with modified fins, tentacles, or legs: anatomically, these structures can include combinations of stiff tissues, extensible tissues, and muscle. Their mechanical behavior during copulation is also diverse: males in some taxa reorient or protrude genital tissues, others inflate them and change their shape, while still other taxa combine these strategies. For these animals, the ability to ready an intromittent organ for copulation and physically interact with a mate's genital tissues is critical to reproductive success, and may be tied to aspects of postcopulatory selection such as sperm competition and sexual conflict. But we know little about their mechanical behavior during copulation. This review surveys mechanical strategies that animals may use for intromittent organ function during intromission and copulation, and discusses how they may perform when their tissues experience stresses in tension, compression, bending, torsion, or shear.