A theoretical analysis of radial wave thermoacoustic engines in cylindrical resonators is developed. Impedance and pressure translation equations are presented for open sections of the resonator and for heat exchangers. Coupled first‐order differential equations are given for pressure and impedance in the temperature gradient supporting engine section (stack). These quantities are used to calculate heat and work flows and to predict engine performance. Theory and design of a variable quality factor resonator for enhanced photoacoustic spectroscopy are presented. The short stack approximation is developed for the radial geometry and is used along with plane‐wave equations to compare refrigerator performance for these two geometries. Results of the comparison are that engines in the plane‐wave geometry are better overall refrigerators when maximizing the coefficient of performance and cooling capacity together.