Topological way of thinking now goes beyond conventional solid materials, and topological characterization of classical mechanical systems governed by Newton's equation of motion begins to attract much attention. To have a deeper insight on physical meaning of topological numbers in mechanical systems, we demonstrate the use of the Hannay angle, a classical counterpart of the Berry phase, as a symmetry protected topological order parameter. We first derive the Hannay angle using a canonical transformation that maps the Newton's equation to the Schr\"{o}dinger type equation. The Hannay angle is then used to characterize a simple spring-mass model topologically with a particular focus on the bulk-edge correspondence and new aspects of the symmetry in a classical system.