Abstract. We compare numerical results obtained from a steady-state MHD model of solar wind¯ow past the terrestrial magnetosphere with documented observations made by the AMPTE/IRM spacecraft on 24 October, 1985, during an inbound crossing of the magnetosheath. Observations indicate that steady conditions prevailed during this about 4 hour-long crossing. The magnetic shear at spacecraft entry into the magnetosphere was 15. A steady density decrease and a concomitant magnetic ®eld pile-up were observed during the 40 min interval just preceding the magnetopause crossing. In this plasma depletion layer (1) the plasma beta dropped to values below unity; (2) the¯ow speed tangential to the magnetopause was enhanced; and (3) the local magnetic ®eld and velocity vectors became increasingly more orthogonal to each other as the magnetopause was approached (Phan et al., 1994). We model parameter variations along a spacecraft orbit approximating that of AMPTE/IRM, which was at slightly southern GSE latitudes and about 1.5 h postnoon Local Time. We model the magnetopause as a tangential discontinuity, as suggested by the observations, and take as input solar wind parameters those measured by AMPTE/IRM just prior to its bow shock crossing. We ®nd that computed ®eld and plasma pro®les across the magnetosheath and plasma depletion layer match all observations closely. Theoretical predictions on stagnation line¯ow near this low-shear magnetopause are con®rmed by the experimental ®nd-ings. Our theory does not give, and the data on this pass do not show, any localized density enhancements in the inner magnetosheath region just outside the plasma depletion layer.