In order to solve the coupling problem of a spatial rigidflexible parallel robot with flexible moving platform, a high-order flexible triangular thick plate element and its continuity constraints were proposed based on the Bézier triangle and absolute nodal coordinate formulation (ANCF). The deformation of the platform was divided by the element and its effects on dynamics were analyzed. The robotic dynamics was established by natural coordinate formulation (NCF) and ANCF. The second-order gradients of the fourth area coordinate were introduced to describe the element deformation in thickness. Besides, the Poisson locking problem was solved accordingly. The Lagrange dynamics equations were solved via the generalized α method and the Newton’s method. The statics and dynamics models of the system were simulated. The results showed that the periodic concave deformation of the moving platform had an impact on the spatial posture of the robot which was exactly consistent with the mechanism layout, mass and load distribution. The coupling mode between the rigid components and flexible moving platform conformed to the nonlinear characteristics of multibody dynamics. The trajectory error was less than 1.2×10-12mm. The errors of dynamics and constraint equations were less than the preset thresholds of 10-6and 10-14, which met the requirements of engineering applications. Meanwhile, the validity and versatility of the method were verified by comparative analysis based on different system parameters.