© 2021 Kaunas University of Technology. All rights reserved.This paper presents mathematical modelling of head-on frontal collisions in which lumped-mass models of cars are validated against full-width rigid barrier (FWRB) and head-on frontal crash tests. The crash tests are selected from the database of the National Highway Traffic Safety Administration (NHTSA). A case study is performed in which a 1999 model year car impacts head-on a 2004 model year car. Using the FWRB frontal crash tests, the loading/unloading stiffnesses and the force-drop ratios of the cars are estimated. The force-drop ratio is introduced to model the transition between the loading and unloading phases of the impact. A mathematical model of head-on frontal collisions is developed which requires as inputs the masses, impact velocities, loading/unloading stiffnesses and the force-drop ratios of the cars. The mathematical model is shown to estimate successfully the key responses in vehicle crashes which are the mean accelerations, deformations and change of velocity of the cars in the head-on collision. The presented approach is analytical and provides hand computation of key responses.