A 9-bits lattice gas model with temperature effect is applied into the simulation of thermoacoustic prime movers. The self-excited oscillation in a thermoacoustic resonant tube has been simulated. The distribution of two-dimensional temperature field and the evolution process of temperature are presented as well. The effects of the length of stack and of its position on acoustic pressure have also been investigated numerically. The simulation results are valuable to the optimum design of stack. The validity of the lattice gas model for a thermoacoustic engine has been verified by the comparison of the simulated and experimental results, which demonstrates that the lattice gas method is suitable for the thermoacoustic simulation.