Dynamical variables are incorporated into Parrinello-Rahman simulations that allow for slipping of the simulation cell relative to its periodic images above and below a specified plane. Equations of motion are derived that show the slip to be determined by the dynamical balance of an internal virial traction and an external glide force. Elements of the phenomenological theory of martensitic transformations---namely, the existence of a habit plane and the fact that the macroscopic deformation of the new phase corresponds to an invariant plane shear---are introduced through the imposition of Lagrangian constraints on the dynamics of the cell and slip variables. A model structural transformation is simulated with and without slip, and with rational and irrational habit planes. The allowance of slip with an irrational habit plane dramatically lowers the barrier to the transformation. The results exhibit a remarkably wide variety of dislocation behavior, including edge and screw dislocations, slip, cross slip, dissociation, and twinning. An example of the physical processes thought to be responsible for the rapid propagation of the phase transformation in steels and shape memory alloys---a glissile dislocation interface---is also observed.