A prosthesis for replacing a mammalian joint, comprising: a first body, including a ball mounted on a shaft; a second body, including a base and a cap which secures to the base, said base and cap each having an inner surface (56, 66) and an outer surface, with the inner surfaces of the base and cap together defining a socket which receives and traps the ball and supports the ball for rotation relative to the second body; characterized in that one of said inner and outer surfaces of said base defines a first groove, and said cap has a first leg projecting in a first direction and being received in said first groove by sliding into said first groove in said first direction; and further in comprising a second leg and a second groove lying parallel to and directly opposite said first leg and said first groove, wherein said first leg defines a first leg opening having an axis extending in a direction that is cross-wise to the first direction, said second leg defines a second leg opening coaxial with the first leg opening, and said base defines a base opening which is aligned with said first leg opening when the base and cap are assembled together; and a pin received in said first leg opening, said second leg opening, and said base opening and extending in the cross-wise direction to secure the cap and base together so that an attempt to slide the cap and base apart from each other in the first direction applies shear forces to the pin; and means for preventing the first leg from moving outwardly away from the first groove in the cross-wise direction when the first leg is received in the first groove; wherein said means for preventing the first leg from moving outwardly away from the first groove includes at least a portion of said base contacting the outer surface of the first leg. a first body, including a ball mounted on a shaft; a second body, including a base and a cap which secures to the base, said base and cap each having an inner surface (56, 66) and an outer surface, with the inner surfaces of the base and cap together defining a socket which receives and traps the ball and supports the ball for rotation relative to the second body; characterized in that one of said inner and outer surfaces of said base defines a first groove, and said cap has a first leg projecting in a first direction and being received in said first groove by sliding into said first groove in said first direction; and further in comprising a second leg and a second groove lying parallel to and directly opposite said first leg and said first groove, wherein said first leg defines a first leg opening having an axis extending in a direction that is cross-wise to the first direction, said second leg defines a second leg opening coaxial with the first leg opening, and said base defines a base opening which is aligned with said first leg opening when the base and cap are assembled together; and a pin received in said first leg opening, said second leg opening, and said base opening and extending in the cross-wise direction to secure the cap and base together so that an attempt to slide the cap and base apart from each other in the first direction applies shear forces to the pin; and means for preventing the first leg from moving outwardly away from the first groove in the cross-wise direction when the first leg is received in the first groove; wherein said means for preventing the first leg from moving outwardly away from the first groove includes at least a portion of said base contacting the outer surface of the first leg.