Anisotropy of the silicon valence band does not lead to any significant anisotropy in the longitudinal hole transport properties, but we find that the transverse mobility is quite anisotropic. The transverse mobility represents the response of charge carriers to a small transverse electric field in the presence of a strong longitudinal field. A detailed, anisotropic Monte Carlo method has been applied to the calculation of the hole transverse differential mobility in silicon. The transverse differential mobility is studied both with regard to variations in the orientation, with respect to the crystalline axes, of the high longitudinal electric field, and with regard to variations in the transverse direction of the mobility, taken in the plane perpendicular to the high electric field. The anisotropy of the valence band causes the transverse differential mobility to strongly vary with respect to the electric field orientation. Symmetry considerations show that the transverse differential mobility is isotropic in the {100} and {111} planes and has twofold rotational symmetry in the {101} planes. Our calculations bear this out. Furthermore, we show that the transverse mobility can be much different from the chordal mobility, in distinction to the case for isotropic band structures. ©1995 American Institute of Physics.