This paper describes a two-dimensional model for self-heating and changes in water levels in bagasse piles of constant rectangular or triangular cross section. (Bagasse is the residue, mainly cellulose, that remains after sugar has been extracted from sugar-cane.) After milling, the bagasse has almost 50% water by weight, as hot water is used to remove the last of the sugar. The bagasse can be used as fuel in electrical power stations, but needs to be dried out before use. This paper discusses the way in which the drying out of a pile depends on the ambient conditions, and the shape and size of the pile. Accordingly, the energy equation, and equations for liquid water, water vapour and oxygen are solved numerically using the method of lines. The equations include terms describing heat conduction, diffusion of water vapour and oxygen, condensation and evaporation and an Arrhenius self-heating term. In addition, recent measurements show that there is also self-heating due to the presence of water in the bagasse, with a maximum effect near 60°C, which is modelled by a modified Arrhenius expression. The local maximum in the heat release curve for the problem leads to approximate steady-state behavior on short time scales that eventually is lost as the pile dries out. This interesting physical behaviour motivates an approximate analytical model for the rate at which liquid water is reduced in the pile. Analytical and numerical results are presented for a variety of pile configurations and somefairly general conclusions are drawn.