One topic of current interest in thermoacoustic research is an annular prime mover Lin et al., J. Acoust. Soc. Am, 100, 2846 (1996). The staring point for this research is an investigation of a constricted annular resonator. A literature search of the field resulted in surprisingly few references. The results of analytic, numerical, and experimental investigations are presented. Introducing a constriction into an annular resonator splits each longitudinal duct mode into two modes, one of a higher frequency with a pressure antinode at the constriction and one at a lower frequency with a velocity antinode near the constriction. The lower mode is more sensitive to changes in the length and porosity of the constriction than the higher mode. Overall agreement between measured and predicted mode shapes and resonance frequencies is very good. It was found that it is necessary to include end corrections at the constriction to get accurate agreement between measured and predicted results.