Entrance pressure losses for the creeping flow of a power-law fluid are calculated for an abrupt contraction of ratio 2. 4, 8 and infinity for both the axisymmetric and planar cases using P2P1 and P2+P1 finite elements. Contrary to some earlier findings in the literature, the entrance pressure loss obtained by using the two different types of finite elements, both of which satisfy the Babuska-Brezzi condition, are found to converge to the same results. The present results also confirm that the variational method of Duda and Vrentas gives excellent upper bounds for both the axisymmetric and planar cases with infinite contraction ratio.