The results of a series of constant pressure and temperature molecular-dynamics (MD) simulation studies based on the rigorous shell particle formulation of the isothermal-isobaric (NpT) ensemble are presented. These MD simulations validate the newly proposed constant pressure equations of motion in which a "shell" particle is used to define uniquely the volume of the system [M. J. Uline and D. S. Corti, J. Chem. Phys. (to be published), preceding paper]. Ensemble averages obtained with the new MD NpT algorithm match the ensemble averages obtained using the previously derived shell particle Monte Carlo NpT method [D. S. Corti, Mol. Phys. 100, 1887 (2002)]. In addition, we also verify that the Hoover NpT MD algorithm [W. G. Hoover, Phys. Rev. A 31, 1695 (1985); 34, 2499 (1986)] generates the correct ensemble averages, though only when periodic boundary conditions are employed. The extension of the shell particle MD algorithm to multicomponent systems is also discussed, in which we show for equilibrium properties that the identity of the shell particle is completely arbitrary when periodic boundary conditions are applied. Self-diffusion coefficients determined with the shell particle equations of motion are also identical to those obtained in other ensembles. Finally, since the mass of the shell particle is known, the system itself, and not a piston of arbitrary mass, controls the time scales for internal pressure and volume fluctuations. We therefore consider the effects of the shell particle on the dynamics of the system. Overall, the shell particle MD algorithm is an effective simulation method for studying systems exposed to a constant external pressure and may provide an advantage over other existing constant pressure approaches when developing nonequilibrium MD methods.