Elastic compression is the process of applying an elastic garment around the leg, supposedly for enhancing the venous flow. However, the response of internal tissues to the external pressure is still partially unknown. In order to improve the scientific knowledge about this topic, a slice of a human leg wearing an elastic garment is modeled by the finite-element method. The elastic properties of the tissues inside the leg are identified thanks to a dedicated approach based on image processing. After calibrating the model with magnetic resonance imaging scans of a volunteer, the pressure transmitted through the internal tissues of the leg is computed. Discrepancies of more than 35% are found from one location to another, showing that the same compression garment cannot be applied for treating deficiencies of the deep venous system or deficiencies of the large superficial veins. Moreover, it is shown that the internal morphology of the human leg plays an important role. Accordingly, the approach presented in this paper may provide useful information for adapting compression garments to the specificity of each patient.