Thermoacoustic heat engines are used to produce sound from heat and to transport heat using sound. Most previous work has concentrated on engines in plane-wave resonators. This paper is about the analysis of engines in radial mode cylindrical resonators. Impedance and pressure translation equations are shown 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 sections. These quantities are used in the computation of energy transfer, and allow for complete analysis of engines with a variety of boundary conditions. Analysis is compared for engines in cylindrical and plane-wave resonators. Previous work in plane-wave resonators has shown that the quality factor Q increases to ∞ as the temperature gradient across the engine becomes sufficiently large. An application of the derived theory is Q and dQ/(denvironment) control of a cylindrical resonator in the design of thermoacoustically enhanced photoacoustic spectrometers that are potentially useful for measuring light absorption by atmospheric aerosols.