A mathematical model of the ignition of cellulose is described which includes both the dry oxidation reaction and also the water-mediated exothermic reaction which is probably hydrolysis. It also takes account of endothermic evaporation of water inside the porous material, exothermic condensation of water vapour and transport of water vapour by diffusion. Appropriate boundary conditions are chosen and the results reported here are restricted to one spatial dimension, but are time dependent. Experimental data obtained recently for bagasse (ground extracted sugar cane) are used as input for the model. However, it is quite likely that the results are of general interest for other cellulose-based materials, many of which are of considerable commercial importance and many of which are believed to undergo spontaneous ignition induced by the presence of water or water vapour. A significant number of experimental observations and conjectures made over a long period are shown to be predictable and interpretable by use of the model, and good agreement with experiment occurs where results are available.