This paper is concerned with shape optimization problems by the boundary element method (BEM) emphasizing the use of a reduced basis reanalysis technique proposed recently by the author. Problems of this class are conventionally carried out iteratively through an optimizer; a sequential quadratic programming-based optimizer is used in this study. The iterative process produces a succession of intermediate designs. Repeated analyses for the systems associated with these intermediate designs using an exact approach such as the LU decomposition method are time consuming if the order of the systems is large. The newly developed reanalysis technique devised for boundary element systems is utilized to enhance the computational efficiency in the repeated system solvings. Presented numerical examples on optimal shape design problems in electric potential distribution and elasticity show that the new reanalysis technique is capable of speeding up the design process without sacrificing the accuracy of the optimal solutions.