In order to solve the compatibility problem occurred during the iteration for the dynamics of a spatial rigid-flexible parallel robot, a nonlinear solution approach was proposed based on a transient kinematic correction method. The nonlinear forward and inverse dynamics of a spatial 3-RRRU parallel robot with flexible links were constructed based on both natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF). The derived models took into account the shear deformation and could describe large deformation for each beam. The transient kinematic correction methods were developed for the both dynamics based on NCF and kinematic model of the robot. The strategy for stable causal solution was also presented based on the aspects such as system energy of the dynamic system. The simulation results showed that the solution precision of inverse dynamics was 10-6 and the compatible error of constraints was 10-8, which met the requirements for engineering applications and could effectively improve the overall convergent performance for the dynamic system. A trajectory tracking experiment was carried out based on a prescribed circular trajectory. Compared with the control strategy on rigid dynamic model, the maximum tracking error and roundness error based on the provided control strategy were decreased by 0.372mm and 1.46mm, respectively. The calculated principal strains of the typical points on the flexible links were at the same levels and variation trends as the measured strains on them. The validity of the developed method was thus verified.