Our purpose is to provide of formulation of the path following problem for multibody kinematic wheeled vehicles aiming to keep the whole vehicle at a reduced distance from a given path, i.e., to reduce the off-tracking distance of the vehicle from the path. In the proposed setting, the stabilization problem for paths of constant curvature is locally solvable by a simple linear feedback law. In order to quantify how much cumbersome a vehicle is along a given path, we provide two different estimates of the off-tracking bound, i.e., of the minimal clearance that has to be left around the path in order for the vehicle lo pass through in case of perfect tracking. Experimental results on a miniature multibody vehicle are reported.