We derive the equations of motion for partially rigid molecules in the isothermal-isobaric N-P-T ensemble. The extended system method introduced by Andersen [J. Chem. Phys. 72, 2384 (1980)] and Nosé [J. Chem. Phys. 81, 511 (1984)] is generalized to the case of discrete mechanical systems subject to geometrical constraints. In our approach all available degrees of freedom are coupled to both the heat and the pressure bath. In this way we take into account that partially rigid molecules can adapt their conformation to volume fluctuations without violating intramolecular constraints. Using projector techniques and Dirac's theory of constrained Hamiltonian dynamics, we derive the equations of motion in Cartesian coordinates and extend the generalized Euler equations for linked rigid bodies [G. R. Kneller and K. Hinsen, Phys. Rev. E 50, 1559 (1994)] to the case of N-P-T dynamics. We prove that the trajectories generated by our equations of motion correspond to the desired N-P-T ensemble.