Experimental data show existence of the proton temperature anisotropy in the dayside magnetosheath (T _⊥p > T _‖p where ⊥ and ‖ denote directions perpendicular and parallel, respectively, to the background magnetic field). The adiabatic MHD model for an anisotropic plasma is known as CGL equations. However, an application of the CGL equations for magnetosheath modeling overestimates the temperature anisotropy T _⊥p /T _‖p . To improve this situation, the CGL model was modified into the bounded anisotropy model [Denton et al., 1994; Gary et al., 1994]. This new class of model takes into account proton pitch angle scattering resulting from a growth of plasma anisotropy instabilities. The present paper contains the calculations of three-dimensional MHD flow around a spherical body with the use of the bounded anisotropy model as well as a comparison between the obtained results and satellite observations of the dayside magnetosheath. The calculated proton temperature anisotropy obtained by the bounded anisotropy model corresponds reasonably to the observed data. The results of the isotropic and anisotropic MHD models are compared. The calculated magnetosheath width is showrn to be greater for the anisotropic double adiabatic model.