A one-dimensional mathematical model for the chemical reaction of a semi-infinite block of coal has been developed and is applied to the problem of simulating underground coal gasification. The model solves conservation equations for mass, momentum, and energy and includes submodels for calculating multicomponent diffusion, based on the Stefan-Maxwell equations and a bi-disperse dusty gas model, the velocity of the drying and char fronts, pyrolysis of the coal, and chemical reaction of char with reactant gases. The assumptions of the model are validated through comparison with experimental measurements of the pyrolysis of large coal particles and the drying, pyrolysis, and gasification of cylindrical coal blocks. Insights into the behavior of coal block gasification are discussed with the aid of model simulations. The capabilities of the model are further demonstrated by simulating cavity growth rates in underground coal gasification under in situ conditions.