A theoretical study is carried out of the combustion of nonspherical carbonaceous particles in the regime of shrinking core reaction. The first problem addressed is the calculation of the pseudosteady temperature and oxidation rate for a particle of given shape. This problem involves the solution of the external diffusion and heat conduction equations with the reaction entering as a boundary condition over the particle surface. Using the boundary integral method, the problem is reformulated as a system of two coupled integral equations which are solved numerically by suitable discretization. The complete transient problem addressing the evolution of particle shape and particle temperature during burnout is similarly formulated by the boundary integral method and solved numerically. Over a broad range of parameters, the pseudosteady particle temperature and rate of oxidation are very nearly equal to those of spherical particles of equal volume and surface area respectively. The transient solutions obtained for parameters typical of pulverized combustion show that during burnout the particle becomes increasingly nonspherical. As expected, nonspherical particles burn faster than spherical particles of the same initial volume, but the difference in burnout times is less than 20% for initial aspect ratios between one and three.