〕 n has hcen proposed in order tD calculate off − axis wave 恥 lds from an ultrasonic transducer as well as on − ax 互 s wave fields . Using this MGB model , we can model three dimens玉 onal ( 3 − D )elastic wave fields radiated fr 〔 ) m an array transducer to a g . olid with an efHcient computational time. 亙 n this paper , brief formulations of th巳 MGB model are described 丘rst and then the accuracy of the MGB model i5 Ghecked ill comparisoll with results of the Rayleigh − Sommerfeld numerical integral mode1 , As applications of the MGB mode1 , we investigate performances of both linear and 皿 a むrix phased array transducers using the MGB inodel . Also the 3 − D wave fields froln the matrix phased array transducer irl solid are visualized