This communication presents experimental data on the time-dependent capillary flow measurements for a high-density polyethylene using a newly developed multipass rheometer (MPR). The experimental data consist of precision pressure measurements on the MPR, which has well-defined fully constrained boundary conditions. A model developed previously by Molenaar and Koopmans [Molenaar, J. and R. J. Koopmans, J. Rheol. 38, 99-109 (1994)] and incorporating melt compressibility has been adapted to suit the MPR boundary conditions and is shown to give good agreement with the experimental data without necessitating the use of any arbitrary adjustable parameters. The results, in particular, show that the experimentally observed pressure relaxation on cessation of the piston movement can be almost entirely attributed to the compressibility of the melt alone and this conclusion is consistent with the findings reported by Hatzikiriakos and Dealy [Hatzikiriakos, S. G. and J. M. Dealy, Polym. Eng. Sci. 34, 493-499 (1994)] for related time-dependent extrusion experimental observations using a conventional capillary rheometer.