The selection of design structure parameters is a critical step for meeting the performance requirement for silicon on insulator (SOI) lateral power devices, especially when multiple design constraints are presented. In this letter, we propose a fully-automated structural design method for SOI lateral power device based on a Bayesian optimization (BO) framework. Given the design target characterized by breakdown voltage (BV) and on-resistance (Ron) specifications, the proposed approach searches for the optimal structure that can satisfy the constraints. The experimental results demonstrate that designs obtained from our optimization framework fall within 5% range from the desired specifications when evaluated using technology computer-aided design (TCAD) simulation, which proves the efficiency of the proposed approach. Besides, the efficiency of our proposed approach is reflected by its runtime which does not exceed 10 minutes for more than 70% of the cases. We believe that this modeling method can greatly accelerate the design exploration process of power devices for designers.