We use a two-dimensional model of the magnetosheath to examine the effects of pressure anisotropy (parallel pressure p∥≠perpendicular pressure p⊥) on magnetosheath structure. The simulation plane includes the Sun-Earth direction and the direction of the interplanetary magnetic field. Thus the crucial effects of field line draping and compression are included. These are the major effects which drive the pressure ratio p⊥/p∥ to a large value. In order to prevent a continual buildup of magnetic flux, a reduced but finite flow of plasma is allowed through the magnetopause. The incident solar wind flow is supermagnetosonic so that a bow shock forms upstream of the magnetopause boundary. The anisotropic pressure simulations use the bounded anisotropy model, which consists of a combination of double adiabatic driving terms and energy exchange due to anisotropy-driven waves. Variations of rsults with respect to input parameters are explored. The results of these simulations are also compared with those of an isotropic pressure simulation with adiabatic equation of state. The major difference appears to be that anisotropic pressure leads to a larger bow shock standoff distance due to the difference in perpendicular pressure (p⊥ versus the isotropic pressure p). In our model, there is a definite correlation between bow shock standoff distance and density depletion, presumably because larger standoff distance allows a greater period of time for density to be depleted by parallel flow. The anisotropic form of the parallel pressure force does not appear to give significantly different results from those found when the negative parallel gradient of the average pressure ((2p⊥+p∥)/3) is substituted, implying that the exact form of the parallel force may not be crucial to global dynamics. ¿ 2000 American Geophysical Union