In this paper we propose minimal solvers for relative pose estimation for two views of the projected silhouettes of two 3D cylinders. Using such line features instead of the standard point feature correspondences means more stable information (i.e. more stable to lighting condition, seasons, changes in environment etc.). Such features also lead to more compact and semantically interpretable representations in 3D as opposed to standard 3D point feature clouds. In this paper we show how it is possible to transform the problem into a simple parameterization where we can represent the problem as a set of six polynomials and provide solvers for their solutions. Through tests in synthetic and real settings we show that the solver is accurate and stable in the presence of added and inherent noise. Our code is publicly available. ( https://github.com/hamburgerlady/cylinder-SfM ).