Like many other assets, housing prices are quite volatile relative to observable changes in fundamentals. If we are going to understand boom-bust housing cycles, we must incorporate housing supply. In this paper, we present a simple model of housing bubbles which predicts that places with more elastic housing supply have fewer and shorter bubbles, with smaller price increases. However, the welfare consequences of bubbles may actually be higher in more elastic places because those places will overbuild more in response to a bubble. The data show that the price run-ups of the 1980s were almost exclusively experienced in cities where housing supply is more inelastic. More elastic places had slightly larger increases in building during that period. Over the past five years, a modest number of more elastic places also experienced large price booms, but as the model suggests, these booms seem to have been quite short. Prices are already moving back towards construction costs in those areas.