The virus bacteriophage T4, from the family Myoviridae, employs an intriguing contractile injection machine to inject its genome into the bacterium Escherichia coli Although the atomic structure of phage T4 is largely understood, the dynamics of its injection machinery remains unknown. This study contributes a system-level model describing the nonlinear dynamics of the phage T4 injection machinery interacting with a host cell. The model employs a continuum representation of the contractile sheath using elastic constants inferred from atomistic molecular-dynamics (MD) simulations. Importantly, the sheath model is coupled to component models representing the remaining structures of the virus and the host cell. The resulting system-level model captures virus-cell interactions as well as competing energetic mechanisms that release and dissipate energy during the injection process. Simulations reveal the dynamical pathway of the injection process as a contraction wave that propagates along the sheath, the energy that powers the injection machinery, the forces responsible for piercing the host cell membrane, and the energy dissipation that controls the timescale of the injection process. These results from the model compare favorably with the available (but limited) experimental measurements.