In this paper we perform a stress wave analysis to determine the forces in hanging cables under the action of powder snow avalanches. Powder avalanches are a serious threat to communities and infrastructure in mountainous regions. They endanger power transmission lines which transport electricity over avalanche prone terrain. Powder avalanches produce an elevated air-blast that induces above ground forces in hanging cables, leading to failure and often the over-turning of the supporting towers. We solve a nonlinear system of three wave equations with appropriate boundary conditions that describes the internal stress state and the cable deformation in three directions. The impact pressures are estimated by simulating powder avalanche motion in three-dimensional terrain. The stress wave model is tested numerically, the obtained results are in good accordance with experimental measurements. We also investigate a possibility of usage of hanging cables as loading sensors to reconstruct powder cloud pressures. For that we formulate an inverse problem, solve it analytically in time-independent case and study numerically the obtained solution.