The work carried out in this paper includes developing and analyzing mathematical models of vehicle structures involved in head-on collisions with different obstacles. Crash analysis of vehicle-to-vehicle and vehicle-to-rigid fixed barrier in full and offset collision events is presented using a mathematical methodology and dynamic responses are obtained with the aid of an analytical approach using Incremental Harmonic Balance Method (IHBM). Moreover, optimized vehicle structures with additional energy absorbers are presented and analyzed. The rail deformation and occupant deceleration are used for interpreting the results. It is proven from numerical simulations that development and analysis of mathematical models are efficient tools for estimating the dynamic response for different frontal collision events. It is also shown that mathematical models are flexible and useful in optimization studies. Furthermore, it is shown that IHBM is an effective method to solve dynamic problems, with strong nonlinear stiffness and dampening characteristics, effectively and accurately. It is also proven that significant improvements to both deformation and deceleration injuries are obtained and crash severity are minimized using optimized vehicle structures.