A family of structure from motion algorithms called the factorization method has been recently developed from the orthographic projection model to the affine camera model. All these algorithms are limited to handling only point features of the image stream. We propose in this paper an algorithm for the recovery of shape and motion from line correspondences by the factorization method with the affine camera. Instead of one step factorization for points, a multi-step factorization method is developed for lines based on the decomposition of the whole shape and motion into three separate substructures. Each of these substructures can then be linearly solved by factorizing the appropriate measurement matrices. It is also established that affine shape and motion with uncalibrated affine cameras can be achieved with at least seven lines over three views, which extends the previous results of Koenderink and Van Doorn for points to lines.