An inflatable compaction tool for consolidating a composite material inside a faceted hollow or tubular mold for a composite part is made from an elastic material. The compaction tool includes relatively flat wall segments conjoined by corner segments that define a sealed chamber. The wall segments curve away from the mold surface toward the midpoint of each wall segment, so that as a pressurized fluid is introduced into the compaction tool, a component of the force exerted on the tool interior surface is transmitted through the wall segments toward the corner segments. Thus, during initial inflation, the corner segments are forced toward the corner regions of the mold before the wall segments contact the composite material, firmly compressing the composite material into the corner regions of the mold before the friction of the wall segments against the composite material inhibits expansion of the corner segments into the mold corner regions.