Dipping, arcuate bands of debris-rich ice outcropping near the margins of glaciers are often interpreted as thrust faults, assumed to originate in zones of longitudinal compression. Identification of thrusts is typically based either on the geometry and sedimentology of the debris bands or on the crystal fabric of surrounding ice, but the physical processes necessary to generate thrusts are rarely evaluated. Herein, we combine a numerical model of compressive ice flow near a glacier margin with theoretical stress and strain rate criteria for ice fracture and stress criteria for frictional slip to determine the conditions necessary for thrust faulting in glaciers. This model is applied to two different glaciological settings where longitudinal compression has been documented: (1) the transition between warm-based and cold-based ice near the terminus of Storglaciären, Sweden, and (2) the downglacier extent of the 1983 surge front of Variegated Glacier where surging ice encountered stagnant ice. Simulations representing the margin of Storglaciären indicate that peak compressive strain rates are six orders of magnitude too small to induce fracture, whereas at Variegated Glacier, strain rates were an order of magnitude too small for compressive fracture. In both groups of simulations, preexisting fractures governed by Coulomb friction are susceptible to slip if they span the ice thickness, are oriented close to the optimal fracture angle, and, in the case of Storglaciären, are subject to water pressures that are a large fraction of ice overburden pressure. Variations about the optimal fracture orientation, low or zero water pressure, high sliding friction coefficient, and limited vertical or lateral fracture extent each tend to suppress thrusting.