Several geologic features suggest the presence of rock glaciers on the surface of Mars. These features include lobate debris aprons, concentric crater fill and lineated valley fill. The lateral extent of these rock glaciers can range from 5 km to over 20 km. A simple time-marching model is developed and used here to demonstrate the ability of ice and ice-rock mixtures to flow under Martian conditions. For temperatures lower than about 220 K, even pure ice becomes too rigid to flow and a glacier 5 km long could not have formed. Results from this model indicate temperatures 20 to 40 K higher than present average midlatitude temperatures (210 K), an ice content of no less than 80%, and a net accumulation rate of at least 1 cm year⁻¹ are required to produce rock glaciers of the size seen on Mars.