Similitude is applied to thermoacoustics without using the acoustic approximation. The equations which are important to thermoacoustics (continuity, motion, and heat transfer) are rewritten in dimensionless form, verifying that the list of dimensionless variables obtained from similitude is complete. Similitude is demonstrated in a thermoacoustic engine using helium, neon, and argon as working fluids, even for large-pressure-amplitude nonlinear behavior which differs significantly from predictions of linear thermoacoustic theory. Measurements are also presented for nitrogen and a helium–argon mixture, in order to reveal the influence of the specific-heat ratio and Prandtl number. Implications of similitude for building scale models are discussed; dimensions, temperatures, or pressures can be scaled.