Recently, many algorithms about automatic driving systems or driver assitance systems have been proposed. Estimation of lane markers and the vanishing point is an important reserch field for these systems. In this paper, we propose a new method to estimate lane markers and the vanishing point based on a dynamics model. In this method, lines that intersect at one point are put at an arbitrary position of the image, and are attracted to lane markers by the force of edge potential. The vanishing point is also estimated at the same time. Experimental results from a real image sequence show the effectiveness of the proposed method.