The paper is concerned with an important issue from the field of thermoacoustics - the numerical modelling of the flow field in the thermoacoustic engine. The presented way of modelling is based on the solution to fundamental fluid mechanics equations that govern the flow of compressible, viscous, and heat-transferring gas. The paper presents the way of modelling the thermoacoustic engine, the way of conducting calculations and the results which illustrate the correctness of the selected computational technique.