Given a control system and a desired property, an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail. In previous work, we considered abstractions of linear and nonlinear analytic control systems while preserving reachability properties. In this paper we consider the abstraction problem for Hamiltonian control systems, that is, we preserve the Hamiltonian structure during the abstraction process. We show how the mechanical structure of Hamiltonian control systems can be exploited to simplify the abstraction computations and we provide conditions under which the local accessibility properties of the abstracted Hamiltonian system are equivalent to the local accessibility properties of the original Hamiltonian control system.