The multiple knife edge model for terrain diffraction problems is extended to apply to solid terrain. The model is constructed by bridging over the spaces between diffracting screens with perfectly reflecting plane surfaces that connect the tops of the diffracting screens. In this way the diffracting screens are hidden from view, and the plane surfaces become a solid, reflecting, model of terrain. Nevertheless, there remains a mathematical similarity with multiple knife edges, and a series solution already known for multiple knife edges can be adapted to the new model. Although bridging over the knife edges adds new modes of propagation, many of these modes make identical contributions to the field, and the final series contains no more terms than for knife edges only. As with knife edges, computing time increses rapidly as a function of the number of knife edges, and the series may not converge if the terrain profile contains valleys. However, valleys can always be removed by means of Babinet's principle. Sample results show that bridging over knife edges results in increased attenuation and a smoother variation with terrain height. A round hill can be approximated, and the resulting attenuation approaches the known attenuation for a round hill, as the number of bridged knife edges increases.