Abstract: Based on the method of integral equation, the unsteady natural supercavitating flow passing a slender wedge is investigated. The unsteady supercavity integral equation of wedge moving with variable velocity in static fluid is obtained. As a special case, the unsteady supercavity integral equation of uniform flow is also obtained. Using the finite difference time discretization method and finite difference method, the integral equations are solved. In the cases of wedge moving with variable velocity, changing wedge angle, changing cavitation number and small perturbing cavitation flow, the numerical results of supercavity’s shape and length are obtained. The results show that unsteady supercavity has two characteristics: retardancy and wave. In the case of wedge moving with variable velocity, the higher the value of acceleration is, the longer the time lags. In the case of wedge moving with uniformly decelerated velocity, cavity is not closed, and the reentrant jet may occur. The higher the perturbing frequency is, the smaller the change of cavity length is, and the longer the time lags. The perturbation spreads as a form of wave along the surface of cavity, and the spread velocity is that of the flow. The results obtained would be useful for the design and analysis of unsteady cavitator under water.