An elasto-plastic impact model based on the p-version finite element method is presented for the collision protection of ocean and offshore structures. The impact force and responses of the impactor-absorber-structure system can be predicted efficiently and automatically. A cost-effective Cellular Reinforced Concrete Absorber (CRCA) is designed to smooth the impact force and absorb the impact energy. Quasi-static tests show that the concrete absorber has an excellent energy absorbing characteristic. The impact experiment of a scaled offshore oil-piping frame with the proposed concrete absorber is carried out. The simulation results of the elasto-plastic model and the p-version finite element method are in good agreement with the experimental ones. Owing to the plastic deformation of the absorber, the impact force during the impact and responses of the structure are considerably reduced. Further, the proposed impact model and the concrete absorber are applied to the design of collision protection of the sheet-pile groin on the Qiantang River used to weaken the famous Qiantang bore.