The effect of hydrostatic pressure on the formability of a model Cu-W metal matrix composite (MMC) was investigated. The main experimental observation was that damaged and codeformed products were obtained from nominally identical Cu-W billets. A criterion for the suppression of damage during hydrostatic extrusion was developed. The resulting critical hydrostatic pressure criterion was estimated from slip line field theory in order to rationalize the experimental observations. The critical hydrostatic pressure for damage suppression in the W fibers depends on the ratio of fracture stress to flow stress. The analysis suggests a very important effect of both the stress state during hydrostatic extrusion and the previous processing history of the composite.