This study assessed the accuracy of using a two-dimensional principal stress analysis compared to a three-dimensional analysis in estimating peak turbulent stresses in complex three-dimensional flows associated with cardiac prostheses. Three-component, coincident laser Doppler anemometer measurements were obtained in steady flow downstream of three prosthetic valves: a St. Jude bileaflet, Bjork-Shiley monostrut tilting disc, and Starr-Edwards ball and cage. Two-dimensional and three-dimensional principal stress analyses were performed to identify local peak stresses. Valves with locally two-dimensional flows exhibited a 10-15% underestimation of the largest measured normal stresses compared to the three-dimensional principal stresses. In nearly all flows, measured shear stresses underestimated peak principal shear stresses by 10-100%. Differences between the two-dimensional and three-dimensional principal stress analysis were less than 10% in locally two-dimensional flows. In three-dimensional flows, the two-dimensional principal stresses typically underestimated three-dimensional values by nearly 20%. However, the agreement of the two-dimensional principal stress with the three-dimensional principal stresses was dependent upon the two velocity-components used in the two-dimensional analysis, and was observed to vary across the valve flow field because of flow structure variation. The use of a two-dimensional principal stress analysis with two-component velocity data obtained from measurements misaligned with the plane of maximum mean flow shear can underpredict maximum shear stresses by as much as 100%.