Europa's surface exhibits numerous small dome-like and lobate features, some of which have been attributed to fluid emplacement of ice or slush on the surface. We perform numerical simulations of non-Newtonian flows to assess the physical conditions required for these features to result from viscous flows. Our simulations indicate that the morphology of an ice flow on Europa will be, at least partially, influenced by pre-existing topography unless the thickness of the flow exceeds that of the underlying topography by at least an order of magnitude. Three classes of features can be identified on Europa. First, some (possibly most) putative flow-like features exhibit no influence from the pre-existing topography such as ridges, although their thicknesses are generally on the same order as those of ridges. Therefore, flow processes probably cannot explain the formation of these features. Second, some observed features show modest influence from the underlying topography. These might be explained by ice flows with wide ranges of parameters (ice temperatures >230 K, effusion rates >10 7 m 3 year −1, and a wide range of grain sizes), although surface uplift (e.g., by diapirism) and in situ disaggregation provide an equally compelling explanation. Third, several observed features are completely confined by pre-existing topographic structures on at least one side; these are the best known candidates for flow features on Europa. If these features resulted from solid-ice flows, then temperatures >260 K and grain sizes <2 μm are required. Such small grain sizes seem unlikely; low-viscosity flows such as ice slurries or brines provide a better explanation for these features. Our results provide theoretical support for the view that many of Europa's lobate features have not resulted from solid-ice flows.