We carry out a first comparison with spacecraft measurements of our recent three‐dimensional, one‐fluid magnetohydrodynamic (MHD) model for the anisotropic magnetosheath [Erkaev et al., 1999], using data acquired by the Wind spacecraft on an inbound magnetosheath pass on December 24, 1994. The spacecraft trajectory was very close to the stagnation streamline, being displaced by less than 1/2 hour from noon and passing at low southern magnetic latitudes (∼4.5°). All quantities downstream of the bow shock are obtained by solving the Rankine‐Hugoniot equations taking the pressure anisotropy into account. In this application of our model we close the MHD equations by a “bounded anisotropy” ansatz using for this purpose the inverse correlation between the proton temperature anisotropy, Ap (≡ Tp⊥/Tp‖− 1), and the proton plasma beta parallel to the magnetic field βp‖ observed on this pass when conditions are steady. In the model the total perpendicular pressure is prescribed and not obtained self‐consistently. For all quantities studied we find very good agreement between the predicted and the observed profiles, indicating that the bounded anisotropy method of closing the magnetosheath equations, first suggested by Denton et al. , is valid and reflects the physics of the magnetosheath well. We assess how sensitive our model results are to different parameters in the Ap = α0βp‖−a1 (a1 > 0) relation, taking for a1 the two limiting values (0.4, 0.5) resulting from the two‐dimensional hybrid simulations of Gary et al. , and varying a0 in the range 0.6 – 0.8. Input solar wind conditions are as measured on this pass. In general, the model profiles depend more strongly on a0 than on a1. In particular, decreasing a0 narrows the width of the plasma depletion layer (PDL) and widens the mirror stable region. For the lowest value of a0, the mirror stable region extends sunward of the outer edge of the PDL. For the other two values of a0, and regardless of the value of a1, it is contained within the PDL. Finally, we also study phenomenological double‐poly tropic laws and find poly tropic indices γ⊥ ≈ 1 and γ‖ ≈ 1.5. These results agree well with those of Hau et al.  inferred from Active Magnetospheric Particle Tracer Explorers/Ion Release Module data on a crossing of the near‐subsolar magnetosheath.