Significance Childbirth is frequently difficult for humans due to a cephalocaudally short and dorsoventrally deep pelvis necessary for upright bipedality and a large neonatal brain. A tight fit between the neonatal head and maternal pelvic dimensions is, however, found not only in humans, but also in some other primate taxa. The rhesus macaques show human-like cephalopelvic proportions. We show that forms of the fetal skull and maternal pelvis during the perinatal period covary in ways to relax the obstructions of childbirth in rhesus macaques. This indicates that morphological covariation of the fetal skull and maternal pelvis could have evolved not only in humans, but also in other primates in parallel, or it could be an example of a catarrhine synapomorphy.