We examine the influence of mesoscale orography or mountains on fronts when the background flow is sufficiently slow and strongly stratified such that the air flows around the sides, rather than over the top, of the orography and when the fronts are sufficiently weak that the potential temperature differences across the frontal zones are much less than the potential temperature differences within each air mass over the height of the orography. These conditions are common for fronts interacting with the European Alps. By drawing together Drazin's (Tellus 13 (1961) 239) classic analysis of low Froude number flows past isolated orography, where the flow is layerwise irrotational, and a material surface description of the weak front, the salient features of the front blocking and deformation by mesoscale orography are captured and studied. When cold fronts are advected past an isolated orographic feature, the distortion of the front is so large near the surface of the orography, that a narrow portion of the front eventually overturns, leading to enhanced precipitation. The general influence of the shape and dimensions of the orography on front deformation and the localised overturning process is examined within an analytical framework.