The hole inversion-layer mobility of strained-SiGe homo- and heterostructure-on-insulator in ultrathin-body MOSFETs is modeled by a microscopic approach. The subband structure of the quasi-2-D hole gas is calculated by solving the 6 x 6 (k) over right arrow center dot (p) over right arrow Schrodinger equation self-consistently with the electrostatic potential. The model includes four important scattering mechanisms: optical phonon scattering, acoustic phonon scattering, alloy scattering, and surface-roughness scattering., The model parameters are calibrated by matching the measured low-field mobility of two particularly selected long-channel pMOSFET cases. The calibrated model reproduces available channel-mobility measurements for many different strained-SiGe-on-insulator structures. For the silicon-on-insulator MOS structures with unstrained-Si channels, the silicon-thickness dependence resulting from our model for the low-field channel mobility agrees with previous publications [1]-[5].