Precession of the hole spin in zinc-blende-type semiconductors in the absence of magnetic field has been investigated. In a noncentrosymmetric lattice the precession is caused by spin-splitting of the valence band. The hole spin quantization axis is shown to depend on the wave vector magnitude and direction, and the spin precession trajectories that run around the quantization axis are found to be ellipses. Analytical solutions are given for high symmetry directions of the wave vector. For a general case, the numerical algorithm is presented. The algorithm takes into account the warping and nonparabolicity of the bands, and may be used to simulate time-dependent precession of the hole spin in semiconductor devices by the Monte Carlo method, for example in the analysis of spin transport in spinFETs or spin lifetime in semiconductors with complex band structure. (c) 2006 Elsevier Ltd. All rights reserved.