The performance of an acoustic transducer is determined by the effects of many design variables, and mostly the influences of these design variables are not linearly independent of each other. To achieve the optimal performance of an acoustic transducer, we must consider the cross-coupled effects of the design variables. In this study, the variation of the performances of underwater acoustic transducer in relation to its structural variables was analyzed. In addition, the new optimal design scheme of an acoustic transducer that could reflect not only individual but also all the cross-coupled effects of multiple structural variables, and could determine the detailed geometry of the transducer with great efficiency and rapidity was developed. The validation of the new optimal design scheme was verified by applying the optimal structure design of a flextensional transducer which are the most common use for high power underwater acoustic transducer. With the finite element analysis(FEA), we analyzed the variation of the resonance frequency, sound pressure, and working depth of a flextensional transducer in relation to its design variables. Through statistical multiple regression analysis of the results, we derived functional forms of the resonance frequency, sound pressure, and working depth in terms of the design variables. By applying the constrained optimization technique, Sequential Quadratic Programming Method of Phenichny and Danilin(SQP-PD), to the derived function, we designed and verified the optimal structure of the Class IV flextensional transducer that could provide the highest sound pressure level and highest working depth at a given operation frequency of 1 kHz.