A two-dimensional, steady-state, flow line model of a debris-covered glacier is developed using mass conservation of debris and ice. Ice deformation is driven by shear stress, estimated from the local ice and debris overburden. Input variables are altitude-dependant ice mass balance, debris mass balance, and a function that modifies the ice mass balance with respect to the amount of surface debris; the model is solved numerically. The model demonstrates that a debris-covered glacier in steady state must be infinitely long and implies that existing debris-covered glaciers are not in steady state. The terminus of a debris-covered glacier is a critical, dynamic region that must constantly advance. The amount of debris input into the model strongly influences the form of the resultant glacier. A relatively large amount of debris produces a debris-covered glacier with a significant amount of ice beneath the debris, a morphology shared by many ice-cored rock glaciers. Less debris input into the system results in a thicker debris cover on top of a thinner layer of ice. Preliminary model results are consistent with observations from the Galena Creek rock glacier, Wyoming.