We quantify the Michel-Dessler magnetotail cross section model, which predicts that the magnetotail flattens due to the anisotropic pressure of draped magnetosheath field lines. We assume steady, typical, solar wind and magnetotail conditions and allow flux to pass through both the current sheet and magnetopause. With these assumptions, our numerical model predicts that the semimajor axis of the elliptical magnetotail cross section at x=-200 RE is 37.8 RE long and lies in the solar ecliptic plane. The semiminor axis (perpendicular to the ecliptic plane) should be no greater than 18.5 RE at this distance. By x=-500 RE, the semimajor and minor axes should be 60 and 11.7 RE long, respectively. The ratio of the major to minor axis lengths depends on the strength of the interplanetary magnetic field (IMF) in the plane transverse to the solar wind flow and is greater for a strong IMF. The reaction time of the distant magnetotail to an impressed IMF variation is on the order of 20 minutes for typical solar wind conditions. The locations of ISEE 3 magnetopause crossings and magnetotail (including boundary layers) observations beyond x=-180 RE are consistent with the model cross section. Our definition of the magnetotail requires B2x≥4(B2y+B2z) or Te>5¿105 K. Furthermore, magnetotail magnetopause boundary normals point nearly parallel to the semiminor axis of the ellipse and therefore indicate strong flattening. We look for, but do not find, evidence of flattening in prior observations of the near-earth magnetotail cross sectional dimensions. Some Pioneer 7 and 8 observations of the deep tail (x<-500 RE) are consistent with magnetotail flattening.