To quantitatively measure the erodibility of soil, including the incipient shear stress and the scouring rate, a new measurement method was proposed. The measurement system contains a cylindrical erosion test apparatus (CETA) and a calculation method of shearing stress. The CETA was developed to measure the relation between the scouring rate and the water velocity, which was mainly composed of a power system, a scouring system, a water circulation system, and a data acquisition system. Using the proposed shearing stress calculation method, the shearing stress by water flow was clarified. On the basis of the proposed new measurement method, single-size soil samples from the Tangjiashan and Yigong landslide dams were collected for measurement of the critical shear stress. The test results demonstrated that the grain size of the cohesionless soil was approximately linear with the critical shearing stress. Furthermore, the erodibility of two samples, the loess from Loess Plateau and coarse grain from Yigong landslide dam, was tested. During the experiment, the loess sample showed a low critical shear stress, τc, of 0.7 N/m2 that was accompanied a dramatic change of erosion process from particle by particle to block by block. By comparison, the critical shear stress τc for the cohesionless soil sample was 3.5 kN/m2, which is consistent the results of measurement of critical shear stress and the measured erosion rate at a constant shear stress and is faster than the loess sample in general. The present test results agreed well with previous experimental results, which further proves the feasibility of the new measurement method and provides a basis for the dam breach analysis due to overtopping.