This paper deals with the optimization of the crossbars, parts of the existing frame of the experimental system of the Alternative SkidCar. This part plays a crucial role and is designed to enable and ensure reduced adhesion conditions between the vehicle and the road. To this end, its optimization targeted here is performed using both analytical calculations and simulations in MSC Adams software, wherein the loading forces and boundary conditions on the frame support wheels are obtained considering the static conditions, as well as the change of the direction of travel. The least favourable load observed was used, later on, as the input value for the strength analysis of the frame. The analysis was performed using the finite element method (FEM) in SolidWorks. Based on the linear and nonlinear analyses performed, the course of stress on the frame arms and critical points with the highest stress concentration were determined. Subsequently, according to the results obtained, a new design for the current frame was proposed and, thereby, warrants greater rigidity, stability and strength to the entire structure, while reducing its weight and maximizing the potential of the selected material. The benefit of the current contribution lies in the optimization of the current frame shape, in terms of the position of weld joints, the location of the reinforcements and the thickness of the material used.