Bridge piers are impacted by autos sometimes. The pier usually has not been destroyed after once impact by auto. But there are few research on damage which will affect pier’s capability, and most relative studies have focused the problems on piers impacted by vessels. The methods involve mainly sutra experience theory, numerical analysis, and experimental method. Owing to the complicacy of the bridge pier impacted by a vessel, there are few research derived with the sutra mechanics model and the piers impacted by autos. The dynamic response is studied here under the assumption of the rigid-plastic small-deformation for the pier impacted by auto. According to the Parkes beam model, the rigid-plastic theoretical solution is deduced. The final deformation is calculated by a practical example for the pier impacted by auto. But pier are has not been destroyed after once impact by auto. But there are few research on damage which will affect pier’s capability, and most relative studies have focused the problems on piers impacted by vessels. The methods involve mainly sutra experience theory, numerical analysis, and experimental method. Owing to the complicacy of the bridge pier impacted by a vessel, there are few research derived with the sutra mechanics model and the piers impacted by autos. The dynamic response is studied here under the assumption of the rigid-plastic small-deformation for the pier impacted by auto. According to the Parkes beam model, the rigid-plastic theoretical solution is deduced. The final deformation is calculated by a practical example for the pier impacted by auto.