An inflation for an automatic milking machine is molded as an integral unit from an elastomeric material. The inflation is formed to have an elongate, hollow barrel (12). The barrel has a substantially triangular cross-sectional shape and terminates in open upper and lower ends. A substantially cylindrical head (14) is molded integrally to the upper end of the barrel (12). The head (14) has a substantially cylindrical side wall. A diaphragm-like mouthpart (20) is positioned across the otherwise open, upper end of the cylindrical side wall, with the mouthpart having a central opening that is adapted to accommodate the teat of an animal to be milked. A transition section (22) is molded in the head (14) so as to connect the upper end of the barrel (12) with an inner surface of the side wall to form an internal, mouthpiece chamber between the transition section (22) and the mouthpart (20). Each of the three longitudinal sidewalls (30) of the triangular-shaped barrel has at least one elongate reinforcement element comprising a relatively narrow raised rib (32) molded integrally along the outer surface thereof. The raised ribs (32) provide added integrity for the sidewalls and greatly improved massage to the teat tissue.