Basal channels are incised troughs formed by elevated melt beneath ice shelves. Channels often coincide with shear margins, suggesting feedbacks between channel formation and shear. However, the effect of channel position and shape on ice-shelf flow has not been systematically explored. We use a model to show that, as expected, channels concentrate deformation and increase ice-shelf flow speeds, in some cases by over 100% at the ice-shelf center and over 80% at the grounding line. The resulting increase in shear can cause stresses around the channels to exceed the threshold for failure, suggesting that rifting, calving and retreat might result. However, channels have different effects depending on their width, depth and position on an ice shelf. Channels in areas where ice shelves are spreading freely have little effect on ice flow, and even channels in confined regions of the shelf do not necessarily alter flow significantly. Nevertheless, if located in areas of vulnerability, particularly in the shear margins near the grounding line, melt channels may alter flow in a way that could lead to catastrophic ice-shelf breakup by mechanically separating shelves from their embayments.