A rigid jounce bumper includes a body and at least one support segment projecting axially from an end of the body. The rigid jounce bumper is formed from a substantially non-elastic material such that the rigid jounce bumper can support axially-applied loads without undergoing substantial axial deflection. The at least one support segment is capable of displacement relative to the body when under laterally-applied loads. A gas spring assembly having such a rigid jounce bumper is also included.