The TOUGH+Millstone simulator has been developed for the analysis of coupled flow, thermal and geomechanical processes associated with the formation and/or dissociation of CH4 hydrates in geological media. It is composed of two constituent codes: (a) a significantly enhanced version of the TOUGH+HYDRATE simulator, v2.0, that accounts for all known flow, physical, thermodynamic and chemical processes associated with the behavior of hydrate-bearing systems undergoing changes and includes the most recent advances in the description of the system properties, coupled seamlessly with (b) Millstone v1.0, a new code that addresses the conceptual, computational and mathematical shortcomings of earlier codes used to describe the geomechanical response of these systems. The capabilities of the TOUGH+Millstone code are demonstrated in the simulation and analysis of the system flow, thermal and geomechanical behavior during gas production from a realistic complex offshore hydrate deposit. In the second part of this series, we describe the Millstone geomechanical simulator. The hydrate-dependent, rate-based poromechanical formulation is presented and solved using a finite element discretization. A novel multimesh coupling scheme is introduced, wherein interpolators are automatically built to transfer data between the finite difference discretization of TOUGH+ and the finite element discretization of Millstone. We provide verification examples against analytic solutions for poroelasticity and a simplified demonstration problem for mechanically induced phase change in a hydrate sediment.