The most common kind of vehicular accident is the low-speed rear-end impact that result in high portion of insurance claims and Whiplash Associated Disorders(WAD). The low-speed collisions have specific characteristics that differ from high speed collisions and must be treated differently This paper presents a simple continuous contact force model for the low-speed rear-end impact to simulate the accelerations, velocities and the contact force as functions of time. A smoothed Coulomb friction force is used to represent the effect of braking, which was found to be significant in simulating low-speed rear end impact. The intervehicular contact force is modeled using nonlinear damping and spring elements with coefficients and exponents. This paper presents how to estimate analytically stiffness and damping coefficients. The exponent of the nonlinear contact force model was determined to match the overall acceleration pulse shape and magnitude. The model can be used to determine ${Delta}Vs$ and peak accelerations for the purpose of accident reconstruction and for injury biomechanics studies.