The uncertainty dynamic response of a spatial flexible beam with large overall motion is investigated in this work. The stochastic differential equation of a three-dimensional beam with large overall motion is derived using the virtual work principle. The polynomial chaos method and a regression-based collocation method are applied to derive a set of completely implicit differential equations. The resulting system of deterministic equations is then solved using the variable rank method to obtain the numerical characteristics of the response. For illustration, the dynamic modeling of a spatial spinning beam with probabilistic geometric and physical parameters is considered. The accuracy and efficiency of the method are verified by comparing the results with those given by the Monte Carlo simulation method. The results indicate that probabilistic parameters affect the dynamic response of the flexible body. It is expected that dynamic modeling with probabilistic parameters can objectively reflect the actual dynamic behavior of elastic systems.