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The Labyrinth in the McMurdo Dry Valleys of Antarctica is characterized by large bedrock channels emerging from beneath the margin of Wright Upper Glacier. To study the morphodynamics of large subglacial channels cut into bedrock, we develop herein a numerical model based on the classical theory of subglacial channels and recent results on bedrock abrasion by saltating bed load. Model results show that bedrock abrasion in subglacial channels with pressurized flow reaches a maximum at an intermediate distance up-ice from the glacier snout for a wide range of sediment grain sizes and sediment loads. Close to the snout, the velocity is too low and the sediment particles cannot be mobilized. Far from the snout, the flow accelerates and sediment is transported in suspension, thus limiting particle impacts at the channel bottom and reducing abrasion. This non-monotonic relationship between subglacial flow and bedrock abrasion produces concave up bottom profiles in subglacial channels and potential cross-section constrictions after channel confluences. Both landforms are present in the bedrock channels of the Labyrinth. We therefore conclude that these geomorphic features are a possible signature of bedrock abrasion, rather than glacial scour, and reflect the complex interplay between transport rate, sediment load, and transport capacity in subglacial channels.