Elastic compression (EC) is a medical treatment which relies on the use of socks to improve the venous return and, thereby, control or treat various vein-related diseases such as ulcers. The beneficial effects of EC have been known for centuries, but their mechanism of action is not totally understood. In order to validate and improve current treatments, it is necessary to determine how the pressure is transmitted from the sock to the vein walls. To address this issue, a patient-specific 3D FE model of the leg under EC was created for a group of six subjects. CT-scans of each patient we re segmented into three regions, namely the superficial soft tissues (mostly adipose and skin), the deep soft tissues (mostly muscles) and the bones, to create the geometry of each model. The local pressure applied by the sock on the skin was estimated using Laplace's law. The hard tissues, considered here as not deformable, were fixed in the model. Soft tissues, namely the adipose tissue and muscle, were defined as isotropic and hyper-elastic (Neo- Hookean strain energy function). The mechanical properties were identified in 3D by an inverse method to fit the FE models on the CT-scans of the legs under EC. The main result is that the mean pressure applied by the EC onto the skin is similar to the pressure applied by the compressed tissues onto the wall of the three main deep veins. This suggests that the mean pressure applied can be used as an indicator of the efficiency of the EC. In a similar way, the maximal hydrostatic pressure can be used to estimate the comfort. Indeed, the results showed that this pressure is inversely proportional to the adipose tissues thickness.