Abstract: Tensor product Bernstein polynomials are basic elements in geometric modeling. To evaluate a point defined by tensor product Bernstein polynomials, de Casteljau algorithm is commonly implemented one direction by one direction, e. g. , first u direction, then v direction, w direction, etc. . In this paper, it is shown that different processing order of parametric directions may result in different computational cost, and for the tensor product de Casteljau algorithm, it is more efficient if we process the directions in the order of increasing degrees of their parametric variables. Experimental results for the tensor product Bernstein polynomials with two and three variables are provided, which are consistent with the theoretical analysis.