A capillary rheometer has been modified, by the addition of a second chamber and valve arrangement below the main die, in order to measure the pressure drops associated with the capillary and entry flows of a number of polymer melts as a function of pressure. The five polymer melts investigated are high- and low-density polyethylene, polypropylene, polymethyl methacrylate and polystyrene, each of which is tested at three temperatures within the normal processing range, at apparent shear rates between 50 and 2500 s(-1) and at mean pressures ranging from atmospheric up to 70 MPa. The capillary pressure drop data are used to obtain shear viscosity functions using conventional capillary rheometry expressions, whilst extensional viscosities are estimated from orifice pressure drop data via the Cogswell-Binding analysis. Both the shear and extensional viscosity curves for all of the polymers are seen to exhibit an exponential pressure dependence that can be characterised by pressure coefficients that are found to be independent of temperature. Trouton ratios for the polymers can be specified by an expression with separable strain rate and pressure dependence terms, the latter of which is again exponential. The pressure coefficients of the Trouton ratio terms then orders the pressure dependence: PS>PMMA>PP>HDPE>LDPE. Our major conclusion is that the Trouton ratio for some of the polymer melts can be a strong function of the pressure, indicating that the variation of extensional properties with pressure can be greater than that of the shear properties.