An apparatus for rolling a bladder includes a support structure, a rolling pin, and a bladder-mounting pin. The apparatus optionally includes a rolling initiator Rolling a bladder includes inserting the bladder while unrolled into an apparatus for rolling a bladder, inserting the bladder between a rolling pin and a bladder-mounting pin of the rolling machine, and rotating the rolling pin to (a) advance a portion of the bladder between the rolling pin and the bladder-mounting pin, (b) roll the portion of the bladder around the bladder-mounting pin, and (c) drive the bladder-mounting pin to rotate in an opposite direction from that of the rolling pin.