The lattice gas automation fluid modelling technique is used to study acoustic streaming phenomena arising from the interaction of sound waves with no-slip boundaries. An outline of a derivation of the macroscopic hydrodynamic equations for a class of lattice gas automata that do and do not include rest particles is presented. Various aspects of the implementation of lattice gas automation models, from both of these classes, on two SIMD parallel computing machines are discussed, including the look-up-table method and the Boolean algebra method for collision updating and the implementation of appropriate boundary conditions. A review and discussion of acoustic streaming is given. Rayleigh's acoustic streaming in a pipe and Milton Andres & Ingard's acoustic streaming at high Reynolds number are considered in some detail. The equations for high Reynolds number acoustic streaming around a cylinder are solved analytically to fourth order by the method of successive approximations. An analysis of the time evolution of sound waves in lattice gas automation models and their interaction with no-slip boundaries is carried out. Comparisons with theoretical predictions show the limits within which the sound waves adhere to linear theory. Quantitative comparisons are made between lattice gas simulations of acoustic streaming phenomena and theoretical predictions for high Reynolds number acoustic streaming in a pipe and around a cylinder. Also given are qualitative comparisons for low Reynolds number acoustic streaming around an obstacle.