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A concept of an under-ride guard comprising an energy dissipater is proposed to enhance the crashworthiness of the light-weight vehicles involved in collisions with heavy freight vehicles. The proposed energy absorbing under-ride guard is analytically modeled incorporating non-linearities due to asymmetric damping, stiffness and kinematics of linkages, using the principles of conservation of momentum and Lagrangian dynamics. A performance criteria based upon the magnitude of intrusion of the car mass, car mass acceleration, and dissipated energy is formulated to investigate the performance benefits of the proposed guard. A multi-variable design optimization is performed to minimize a weighted function of performance variables and to determine the optimal asymmetric damping and stiffness properties of the guard.