Channels of inferred subglacial fluvial origin ("channelways") are conspicuous across the recently deglaciated eastern Puget Lowland of Washington State. Exploiting the unusually well defined geometry of the former Puget-lobe ice sheet, we have reconstructed the subglacial hydraulic head in this region to better understand the location and orientation of these channels. We used established principles of channelized water flow under static ice because a three-dimensional linear-viscous ice model shows that sliding-induced pressure variations can be ignored at all but the smallest scales of individual landforms. Two types of predicted subglacial flow paths emerge. One drained continuously from the interior toward the ice-sheet margin; the other diverted water into a series of valleys in the flanking Cascade Range, forming ice-marginal lakes that discharged episodically and probably catastrophically. These reconstructed flow paths correlate very well with the independently mapped distribution of channelways, and also of ice-marginal lakes, throughout this area. Our study suggests that the formation and preservation of these landforms require both the concentration of subglacial water, notably near ablation-zone ice margins, and favorable preglacial bed-rock topography. Where these elements occur together, landforms of subglacial fluvial origin should be recognizable across the now-exposed beds of other former ice sheets as well.