The influence of external pressure on the dynamics of crystallization is examined by considering a solid-liquid two-phase system in a cylinder closed by a piston. The dynamic equations are derived using three methods, namely, Rational Thermodynamics (Liu's procedure), the Matrix Model, and the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) formalism. The constitutive relation for the multiphase pressure on the piston is identical for all three methods, whereas some aspects of the result for the phase change dynamics differ. The rational thermodynamics treatment constrains the phase change dynamics of only those structural variables that enter into the dissipation inequality, whereas the other two formalisms make statements about the phase change of all structural variables. Nevertheless, all three methods show, first, that the phase change happens instantaneously at constant volume and, second, where morphological detail can be built into the model without violating thermodynamic principles. It is discussed how an appropriate choice of the morphological variables allows one to incorporate impingement of crystals and depletion zone effects, as well as to distinguish crystal shapes. (C) 2004 Elsevier B.V. All rights reserved.