A small scale thermoacoustic Stirling engine (TASHE) is simulated according to the linear thermoacoustic theory. The computed results show that in a small scale thermoacoustic Stirling heat engine, the diameter of the resonance tube might have important influences on the working frequency and the performance of the engine, which are always neglected in a large scale system. Likewise, the analysis and experimental results show that in order to obtain better engine performance, the diameter of the resonance tube must be chosen appropriately according to the looped tube dimension and the input heating power. This provides an effective way to miniaturize the thermoacoustic Stirling heat engine. According to the computation and analysis, a small scale engine was built, the resonance tube length and diameter of which were about 350 mm and 20 mm, respectively, and the working frequency was about 282 Hz. When the input heating power was about 637 W, the maximal peak to peak pressure amplitude and pressure ratio reached 0.22 MPa and 1.116, respectively, which were able to drive a thermoacoustic refrigerator or an electrical generator.