Plasma sheaths driven by radio-frequency voltages occur frequently, in contexts ranging from plasma processing applications to magnetically confined fusion experiments. These sheaths are crucial because they dominantly affect impedance, power absorption, ion acceleration and sometimes the stability of the nearby plasma. An analytical understanding of sheath behavior is therefore important, both intrinsically and as an element in more elaborate theoretical structures. In practice, these radio-frequency sheaths are commonly excited by highly anharmonic waveforms, but no analytical model exists for this general case. In this letter we present a mathematically simple sheath model that can be solved for essentially arbitrary excitation waveforms. We show that this model is in good agreement with earlier models for single frequency excitation, and we show by example how to develop a solution for a complex wave form. This solution is in good agreement with simulation data. This simple and accurate model is likely to have wide application.