This work focuses on the analysis of the vertical dynamics of an agricultural tractor, investigating the influence of suspensions' parameters on riding comfort and contact forces. The use of lugged tires coupled with the operation over banked, irregular and deformable tracks, determines significant levels of vertical acceleration over several components of the tractor. These operating conditions have a direct effect on the driver, whose alertness and efficiency are undermined by the exposure to high levels of acceleration for a long time. Secondly, variations of the normal and traction forces provided by the tires affect the quality of tillage and other operations. The paper presents a multi-body vehicle model of a tractor interfaced with a tire-soil contact model allowing to take into account soil's deformation and tread pattern design. The proposed model was used to perform a numerical analysis of a commercial tractor equipped with two different sets of commercial tires, performing tillage operations on a deformable soil; the analysis aimed at optimizing the suspensions' parameters: in particular damping of seat, cabin and front suspensions were changed to determine the possible improvement with respect to the nominal configuration.