The application of the lattice Boltzmann model to simulating nonlinear propagative acoustic waves is considered. The lattice Boltzmann model, and its application to the study of nonlinear sound propagation, are discussed. Lattice Boltzmann simulations of the development of a shock front are performed when a sound wave is emitted from a high-amplitude sinusoidal source. For a number of parameters, representing different physical situations, the wave development is compared with inviscid shock theory and with the solution of Burgers' equation for a fully viscous fluid. The simulations show good agreement with Burgers' equation and with the inviscid theory when propagation at high Reynolds number is considered. These results suggest that the lattice Boltzmann model is a useful technique for studying a range of problems in nonlinear acoustics.