Inflatable penises have evolved independently at least four times in amniotes, specifically in mammals, turtles, squamates, and the archosaurs. Males in these lineages therefore share the functional problem of building a penis out of soft and flexible tissues that can increase its flexural stiffness and resist bending during copulation. Research on penile erectile tissues in mammals and turtles shows that these two taxa have convergently evolved an axial orthogonal array of collagen fibers to reinforce the penis during erection and copulation; in both lineages, the collagen fibers in the array are crimped and folded in the flaccid penis. Collagen fiber straightening during erection increases the stiffness of the tissue and allows changes in penile radius that increase its second moment of area: both of these changes increase the flexural stiffness of the penis as a whole. And once erect, axial orthogonal arrays have the highest flexural stiffness of any fiber arrangement. The high degree of anatomical convergence (to the level of microanatomical features) within mammals and turtles suggests that the stiffness requirements for copulation produce an extremely restrictive selective regime in organisms that evolve inflatable penises.