To assess the feasibility of high-pressure simulation of biomolecular systems, we discuss some practical aspects of molecular dynamics simulation techniques at constant pressure, and temperature. We compare the extended Lagrangian (EL) method, initially developed by Andersen(1) for sampling from well-defined statistical mechanical ensembles, with the method by Berendsen et al.,(2) where temperature and/or pressure are kept constant by weakly coupling (WC) the system to external thermal and pressure baths. We examine the convergence of the volume and of its fluctuations (related to the system compressibility) in both approaches and compute the statistical efficiency of the two methods. Also, the influence on computed observables and fluctuations of the adjustable parameters entering the equation of motions in both approaches is discussed. Systems of increasing complexity from liquid argon to a solvated protein are examined. Remarkably, we find that observables such as volume and enthalpy obtained by extended Lagrangian and weak coupling simulations at the same thermodynamic point are within statistical error of each other. However, for values of the pressure and temperature coupling parameters used commonly in simulation of biomolecules, the statistical inefficiency of the WC approach is higher than for the EL method. This was confirmed in the study of the solvated protein, We find also that at equal computational expense the compressibility is calculated from fluctuation formulas and finite differences with similar precisions. Finally, we observe that when the solvated protein undergoes a sudden pressure increase, the volume relaxes involving two time scales : a slower one with a half-time close to 20 ps due probably to the protein internal relaxation and a faster one with a half-time of about 300 fs attributed to the solvent water. Thus, the equilibration to a new pressure of a solvated protein is 2 orders of magnitude slower than for water but occurs on a time scale manageable by current molecular dynamics simulation techniques.