We use a two dimensional model of the magnetosheath, not including the bow shock, to examine the effects of pressure anisotropy on magnetosheath structure. The simulation plane includes the Earth--Sun direction and that of the incoming interplanetary magnetic field. Thus the crucial physical effects of compression and draping are both included. Flow of magnetic flux and plasma around the magnetopause in the third direction is modeled by a finite electric field at the magnetopause which allows plasma and flux to cross the magnetopause. The magnetopause is a flux surface, which is a reasonable approximation for low shear conditions. We use three models for the plasma pressure: isotropic adiabatic, double adiabatic and the bounded anisotropy model [Denton et al., 1994; 1995>. In an isotropic plasma, density depletion results from draping which produces parallel (to B) flow around the magnetopause. This flow is greatly enhanced by the parallel pressure gradient. In an anisotropic plasma, enhancement of density depletion comes about not by the ordinary parallel pressure gradient but by action of the mirror force. Because this mirror force is large for an anisotropic plasma, use of double adiabatic of bounded anisotropy pressure equations results in greater density depletion than that resulting from isotropic adiabatic theory. ¿ American Geophysical Union 1996