The hole inversion layer mobility of in-plane uniaxially stressed Si is modeled by a microscopic approach. For an arbitrary crystallographic surface orientation the two dimensional hole gas subband structure is calculated by solving the 6 x 6 (k) over right arrow . (p) over right arrow Schrodinger equation self-consistently with the electrostatic potential. Three important scattering mechanisms are included: optical phonon scattering, acoustic phonon scattering and Surface roughness scattering. The model parameters are calibrated by matching the measured low-field mobility of relaxed Si on (0 0 1) Si wafers. The calibrated model reproduces available channel mobility measurements for unstrained and uniaxially stressed Si on (0 0 1), (1 1 1) and (1 1 0) Substrates. (C) 2008 Elsevier Ltd. All rights reserved.