The spherically curved square element phased array design for ultrasound surgery was studied in several of its important aspects. A method for determining the spatial limitations of the multiple-foci region was developed for spherically curved phased arrays. The effects on the ultrasound fields of varying the phases and the amplitudes at control points were investigated. It was found that the phases and the magnitudes of control points have an impact on the ultrasound field distributions. The effects of multiple-foci spacing, pulse duration, and maximum temperature on the size and shape of necrosed tissue were investigated. For a spherically curved phased array with an 8 cm radius of curvature, an 8.8 x 8.8 cm2 projected area, and a 1.5 MHz operating frequency, the minimum number of phased array elements that could produce the largest acceptable necrosed tissue volume was 256. The tissue volume necrosed during the sonication could be increased to approximately 1 x 1 x 3 cm3 with this array.