The purpose of this study was to estimate wall shear stress (WSS) in individual vessels of the venous circulation of the calf and quantify the effects of elastic compression based on change of vessel geometry and velocity waveform. The great saphenous vein and either a peroneal or posterior tibial vein have been imaged in four healthy subjects using magnetic resonance imaging, with and without the presence of a grade 1 medical stocking. Flow through image-based reconstructed geometries was numerically simulated for both a range of steady flow rates and ultrasound derived transient velocity waveforms, scaled to give a standardised time averaged flow rate. For steady flow the stocking produced an average percentage increase in mean WSS of approximately 100% in the great saphenous vein across a range of 0.125 ml s^-1 to 1.25 ml s^-1. The percentage increase in the peroneal/posterior tibial veins varied from 490% to 650% across a range of 0.5 ml s^-1 to 5 ml s^-1. In addition, application of the stocking eliminated periods of very low or zero flow from the transient waveforms. The average minimum value of WSS in all vessels without the stocking was less than 0.1 Pa. With the stocking this was increased to 0.7 Pa in the great saphenous and 0.9 Pa in the peroneal/posterior tibial veins. The pathophysiological effects of these changes are discussed. In conclusion, the flight stocking was effective in raising venous WSS levels in prone subjects and this effect was much more pronounced in the deep vessels. The stocking also tended to prevent cessation of flow during periods of increased downstream pressure produced by respiration.