Design variable reduction is a very important technique for obtaining efficient structural optimization using a mathematical programming technique. Two reduction techniques based on the isoparametric interpolation method and the trigonometic series interpolation method are suggested. The minimum compliance design problem subjected to volume constraint and its sensitivity analysis are formulated for these reduction techniques, based on the boundary element analysis. These techniques concatenated with the sequential quadratic programming method are applied to determine hole shapes in the plates under biaxial uniform loading with different stress ratios and a shape of a multiconnected cantilever structure. From these numerical results, the validity and applicability of the reduction techniques are confirmed.