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This paper proposes a robust method for recovery of motion and structure from two image sequences taken by stereo cameras undergoing a planar motion. The feature correspondence between images are extracted and refined automatically by the relation of the stereo cameras and the property of the motion. To improve the robustness, the random sample consensus (RANSAC) algorithm is adopted in the motion and structure estimation. Unlike other researchers to recover of epipolar geometry, here we use it to recover the 2D motion and to exclude the outliers not only out of the epipolar lines but also in them. Also the spirit of RANSAC is used in structure estimation to exclude the outlier from the sequence view. The most important contribution of this work is a way to make this estimation scheme more robust and efficient so as to be used in real applications. The experiments indoor and outdoor have been done to verify the feasibility of the algorithm. The results show the algorithm is robust and efficient for applications in planar motion.