Collision‐dominated transverse magnetohydrodynamic shock structure is examined for the case where the magnetic fields are strong enough to make the plasma transport properties anisotropic. Different electron and ion temperatures are assumed. A singular perturbation approach is taken to obtain an analytic description of the steady shock structure. For very high Mach numbers (i.e.,us≫ai, upstream sound speed) the shock width is given by&Dgr;s≅2×10−2 us4n1  1 − 32 &ggr;+1&ggr;−1 bs2us2 (m)in hydrogen whereus, n1, b1, and&ggr;are the shock speed, upstream number density, Alfve´n speed, and ratio of specific heats, respectively, and where(us/b1)2≳ 12has been assumed. This shock width is at least an order of magnitude less than shock widths calculated at the same shock speeds with isotropic dissipation coefficients. The results agree reasonably well with previous computer simulations and experimental data.