The shape of the front of a lava flow is controlled by the forces acting on the lava and, in turn, controls the flow dynamics. We present an analysis of the shape of the front of an advancing lava flow, considering both a Newtonian fluid and a Bingham fluid, which is the most commonly used non-Newtonian rheological model for lava. We assume than the flow front is moving at constant velocity on a sloping plane. The flow is considered as having an infinite extent perpendicularly to the flow direction, so that the problem is two-dimensional. The forces producing the flow advance are the gravity force and the pressure gradient due to the curvature of the flow surface. The differential equation for the shape of the front is solved analytically both in the case of a Newtonian fluid and in the case of the Bingham fluid. Since the fluid is considered as homogeneous and isothermal, the calculated shape applies to the fluid core of the flow front. The presence of a solid crust at the top of the flow, producing variable amounts of solid debris at the flow snout, alters the observable shape of the front and is taken into account in order to compare the model front shapes to those observed in the field.