Leaf springs are essential elements in the suspension systems of vehicles including sport utility vehicles(SUV), trucks, and railroad vehicles. Accurate modeling of the leaf springs is essential in evaluating ride comfort, braking, NVH, and stability. The floating frame of reference formulation is employed to accurately model the leaf springs nonlinearities. Vehicle rollover may result from severe braking during lane changes, cornering, and maneuvering. The braking-induced-steering can lead to rollover instability. In this study, the dynamics of a detailed SUV model is investigated by using the model in a parametric study to examine the effect of various design configurations. To study the dynamics of very flexible leaf springs, the absolute nodal coordinate formulation (ANCF) is used. A shear-deformable beam element is developed to analyze large rotation and large deformation problems. Using the ANCF, nonlinear strain-displacement relationships are used to define the elastic forces. The beam mass matrix remains constant while the centrifugal and Coriolis forces are zero. The new ANCF beam wa used to analyze very flexible leaf springs in this investigation.