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Abstract: Ponding on flat or nearly flat roofs keeps drawing attention due to the large number of collapses over the course of years. Though at present computer programs start to offer functionality to check the sensitivity of roofs for water accumulation, true insight appears to be missing on the very nature of the phenomenon. In this paper two models are presented for regular grids, that fill the understanding gap: the piston–spring model for rather stiff roofs and the bar–spring model for extremely flexible ones. The models apply for horizontal roofs, sloped roofs, roofs with initial deflection due to permanent load, camber and composed roofs. Rain showers are considered, so heavy that the water level keeps staying at the specified height of the emergency discharge (full ponding). The case of a specified limited water volume (partial ponding) is not considered. Full ponding is studied for both fully filled roofs and partially filled roofs. The derived theory brings to light that two main roof categories exist; one stress-dominated and one stability-dominated. Four application examples demonstrate that the models are easy-to-use design tools for structural engineers. The derived theory clarifies the effect of the profiled steel roof sheeting on safety and other practical hints are included in the paper. [Copyright &y& Elsevier]