In curve and surface modeling, Bernstein polynomial compositions are widely used for various geometric operations. So it is important to investigate them both in theory and practice. The problems are investigated by using polynomial interpolation and symbolic computation, and the proposed method is applied for curve and surface cases. Compared with two existing methods, the proposed method has the advantages on computational cost, coding efficiency, storage cost. However its numerical accuracy is lower than the method based on the generalized de Casteljau algorithm.