By introducing new cell dynamics to the Parrinello-Rahman method, we propose extended methods for molecular dynamics simulations under hydrostatic pressure and/or isostress. The new method leads straightforwardly to the virial theorem. The obtained equations of motions are invariant under transformations between spatially periodic simulation cells. Molecular dynamics simulations of the crystalline phases of spheres and elongated molecules are conducted. (C) 2003 American Institute of Physics.