In this work we address the problem of occlusion in tracking multiple 3D objects in a known environment and propose a new approach for tracking vehicles in road traffic scenes using an explicit occlusion reasoning step. We employ a contour tracker based on intensity and motion boundaries. The motion of the contour of the vehicles in the image is assumed to be well describable by an affine motion model with a translation and a change in scale. A vehicle contour is represented by closed cubic splines the position and motion of which is estimated along the image sequence. In order to employ linear Kalman Filters we decompose the estimation process in two filters: one for estimating the affine motion parameters and one for estimating the shape of the contours of the vehicles. Occlusion detection is performed by intersecting the depth ordered regions associated to the objects. The intersection part is then excluded in the motion and shape estimation. This procedure also improves the shape estimation in case of adjacent objects since occlusion detection is performed on slightly enlarged regions. In this way we obtain robust motion estimates and trajectories for vehicles even in the case of occlusions, as we show in some experiments with real world traffic scenes.