This article proposed an estimation method of Young's modulus of carotid artery to evaluate the progressiveness of arteriosclerosis. Both carotid artery and the surrounding tissues are modeled by the compound cylinder model with view point of strength of materials. The model gives the amount of theoretical displacement of both carotid artery and the surrounding tissues from diastolic phase to systolic phase. Young's modulus of the carotid artery that is one of the model parameters can be obtained by fitting the theoretical displacement to the measurement value most precisely. It is shown that Young's modules estimated by the propose method agrees with those measured in other literatures.