Combining the interval theory with the second order expansion of Taylor method for solving uncertain nonlinear structure dynamics,we derived an effective numerical method to solve Uncertain SingleDegreeofFreedom Hysteretic System, whose uncertainty was caused by the stochastic hysteretic loop itself, and obtained the upper boundary and the lower boundary of the response. The result of the proposed method was close to that obtained by probabilistic approach.When the uncertainty of nonlinear vibration systems is caused by the stochastic hysteretic loop itself, and the uncertain statistics information of the stochastic hysteretic loop itself is so little that the probabilistic approach is unsuitable, the proposed method can still provide reference for the engineering.