The paper presents a 7-degree-of-freedom dynamic model created for the analysis of the behavior of a vehicle equipped with a rigid rear axle. The proposed model captures the primary motions of the sprung mass (roll, pitch, and vertical displacement), as well as the vertical motion of the unsprung masses associated with the axles, thus providing a detailed description of the interaction between the vehicle and the road surface. The complexity of the analysis is significant, as the coupling effects between roll and vertical motions become pronounced, while lateral stability is strongly influenced by the distribution of stiffness and damping characteristics. The mathematical model is formulated as a system of coupled differential equations, highlighting the interdependencies among the degrees of freedom and enabling the investigation of vehicle response to road profile excitations. Relevant scenarios for the assessment of ride comfort and stability are analyzed, emphasizing the influence of design parameters on the dynamic behavior. The obtained results demonstrate that the 7-degree-of-freedom model represents an effective compromise between complexity and accuracy, being capable of capturing phenomena specific to vehicles with a rigid rear axle, particularly in the absence of additional roll control systems. The study proves useful for suspension parameter optimization, as well as for the analysis of dynamic behavior in the early stages of vehicle design.