Abstract: Due to the influence of manufacturing precision and space environment, the uncertainty of characteristic parameters such as geometric and material parameters of space manipulator reduces the motion accuracy and reliability of the manipulator system. In order to study the influence of uncertain parameters and joint clearance on the dynamic response of the manipulator, and the challenge of obtaining accurate probabilistic reliability due to insufficient experimental sample data of space manipulators. In this paper, a dynamic model and a non-probabilistic reliability calculation method for a flexible manipulator with joint clearance and uncertain parameters are established. Firstly, the clearance model is established by combining the collision force model and the state function, the deformation of the flexible manipulator is described by the hypothetical mode method. Then, utilizing the Lagrange method to establish the dynamic model of the flexible manipulator with joint clearance. On this basis, considering the uncertainty of the manipulator parameters, the uncertain parameters of the system are illustrated as interval variables to establish the uncertain dynamic model of the manipulator. Moreover, the dynamic equations of the flexible manipulator with interval variables are calculated by the interval algorithm based on Chebyshev polynomials. In response to the issue of motion reliability of the space manipulator, a limit state function and four types of non-probabilistic reliability method are presented respectively. Finally, simulation analysis was conducted based on the proposed uncertainty dynamics model and four non-probabilistic reliability calculation methods. The numerical simulation is implemented to verify the effectiveness of the proposed uncertain dynamic model and non-probabilistic reliability methods. The proposed method can achieve accurate dynamic prediction and non-probabilistic reliability analysis, and the possibility method presents higher computational efficiency compared to the Monte Carlo method.