This paper presents an indirect approach to estimating the mechanical properties of tissues surrounding the arterial vessels using ultrasound (US) Doppler measurements combined with an inverse problem-solving method. The geometry of the structure and the dynamic behavior of the inner fluid are first evaluated using a novel dual-beam US system. A numerical phantom associated with a parametric finite element simulator that calculates the hydrodynamic pressure and the displacement on the walls' boundaries is then built. The simulation results are iteratively compared to the US measurement results to deduce the value of the unknown parameters, i.e., the Young's modulus and the pressure resulting from the downstream load. The feasibility of the proposed approach was experimentally tested in vitro using a phantom composed of a latex tube surrounded by a cryogel tissue-mimicking material.