A method of supporting a pressure bearing wall against a pressure differential applied across the wall can include positioning a support structure proximate the pressure bearing wall, the support structure having a support surface formed thereon, and the support surface contacting the pressure bearing wall and supporting the wall against the pressure differential. A pressure bearing housing assembly can include a pressure bearing wall and a support structure which supports the pressure bearing wall against a pressure differential applied across the wall. A well system can comprise a well tool including a pressure bearing housing assembly exposed to pressure in a wellbore, whereby a pressure differential is applied across a pressure bearing wall of the housing assembly, the pressure bearing wall being supported against the pressure differential by a support structure.