Introducers for introducing a surgical circular stapler into a patient. Various embodiments comprise cover members that are applied over a stapling head portion of the circular stapler. In some embodiments, the cover members are fabricated from a flexible stretchable material and have a bumper portion that protrudes distally beyond the distal face of the stapling head. The staples may be fired through the cover member and the balance of the cover member is withdrawn from the patient with the stapling head. Other cover embodiments are selectively movable from a position wherein the distal face of the stapling head is covered and other positions wherein the distal face of the stapling head is exposed.