This paper applies the standard rational expectations competitive storage model to the study of thirteen commodities. It explains the skewness, and the existence of rare but violent explosions in prices, coupled with a high degree of price autocorrelation in more normal times. A central feature of the model is the explicit recognition of the fact that it is impossible for the market as a whole to carry negative inventories, and this introduces an essential non-linearity which carries through into non-linearity of the predicted commodity price series. For most of the thirteen commodity prices, the behaviour of prices from one year to the next conforms to the predictions of the theory about conditional expectations and conditional variances. However, given the non-linearity both of the model and of the actual prices, such conformity is not enough to ensure that the theory yields a complete account of the data. In particular, the analysis does not yield a fully satisfactory explanation for the high autocorrelation observed in the data.