The application of superposition theory to capillary and entry pressure drop data for a number of polymer melts, measured at elevated pressures, is investigated in order to gain information on their pressure dependencies in both shear and elongational flows. To facilitate the study a capillary rheometer has been modified, by fitting a second chamber and valve arrangement below the main die, which allows the pressure downstream of the relevant capillary and orifice dies to be raised so that the mean pressure associated with each die can be varied. Five polymer melts are investigated: high-density polyethylene (HDPE), low-density polyethylene (LDPE), polypropylene (PP), polymethyl methacrylate (PMMA) and polystyrene (PS). Each of these are 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 80 MPa. Time-temperature-pressure superposition is applied to the capillary and orifice pressure drop data for each of the polymers and the resulting pressure coefficients are found to be independent of temperature. The superposition is found to hold for all of the samples considered in both shear and elongational flow, although the degree of fit is best for the HDPE and LDPE. The resulting pressure coefficients for the shear and elongational flows then order the pressure dependencies of the polymers as follows: PS > PMMA > PP > LDPE > HDPE. It is demonstrated how this ordering is determined by the molecular structure of the polymers. However, the most significant result is that for each polymer the shear temperature and pressure coefficients are of similar value to those of elongation, with the exception of PS that has considerably greater coefficients in elongation particularly for temperature. Complementary results for single and multigrade oils are also included, in the appendix.