Previous works have emphasized the significant influence of the solar wind Alfvén Mach number (MA) on magnetospheric dynamics. Here we report statistical, observational results that pertain to changes in the magnetosheath flow distribution and magnetopause shape as a function of solar wind MA and interplanetary magnetic field (IMF) clock angle orientation. We use all Cluster 1 data in the magnetosheath during the period 2001–2010, using an appropriate spatial superposition procedure, to produce magnetosheath flow distributions as a function of location in the magnetosheath relative to the IMF and other parameters. The results demonstrate that enhanced flows in the magnetosheath are expected at locations quasi-perpendicular to the IMF direction in the plane perpendicular to the Sun-Earth line; in other words, for the special case of a northward IMF, enhanced flows are observed on the dawn and dusk flanks of the magnetosphere, while much lower flows are observed above the poles. The largest flows are adjacent to the magnetopause. Using appropriate magnetopause crossing lists (for both high and low MA), we also investigate the changes in magnetopause shape as a function of solar wind MA and IMF orientation. Comparing observed magnetopause crossings with predicted positions from an axisymmetric semi-empirical model, we statistically show that the magnetopause is generally circular during high MA, while is it elongated (albeit with moderate statistical significance) along the direction of the IMF during low MA. These findings are consistent with enhanced magnetic forces that prevail in the magnetosheath during low MA. The component of the magnetic forces parallel to the magnetopause produces the enhanced flows along and adjacent to the magnetopause, while the component normal to the magnetopause exerts an asymmetric pressure on the magnetopause that deforms it into an elongated shape.