Noninvasive surgery using high-powered, focused ultrasound transducers in conjunction with magnetic resonance imaging has been shown to be feasible in previous studies. For clinical treatments, the geometry of standard MRI equipment limits the space available for ultrasound surgical equipment. This space requirement can be reduced in one dimension by using phased arrays to control the focal depth, thus eliminating the space required for the motion of a fixed focus transducer. Because of its symmetry, an annular array is ideal for changing the focal depth. Previous works have simulated, built, and characterized various concentric-ring transducers; however, no study has thoroughly examined the potential and limitations of the concentric-ring design for MRI guided ultrasound surgery. The present work is a systematic examination of the capabilities of the concentric-ring array, using numerical simulations to predict the power field, temperature distribution, and accumulated thermal dose. The results presented here illustrate the effects of ring size, center-to-center spacing configurations, number of rings, and radius of curvature on transducer performance. A 10-cm radius of curvature transducer with 14 evenly spaced rings has been built and characterized in order to verify the accuracy of the numerical simulations. The pressure-squared fields produced by this transducer are in excellent agreement with the simulated fields.