Abstract: A pseudo-dynamic solution algorithm is developed for mechanism systems in civil engineering which are with both larger elastic deformation and mechanism motion in its construction and assembly processes. The proposed method is adaptive for such motion and deflection hybrid problems in which the dynamic effect can be omitted. Geometric nonlinear finite elements are used in the mechanism system discretization. The formulation is based on dynamic kinematical equations, in which the kinematical damping is introduced in the Newmark direct integration process and the dynamic relaxation method is combined. The simulation program is developed to carry out numerical solutions. Numerical results show that the proposed method can effectively trace the whole process of motion and deflection hybrid cases of mechanical assemblies.