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Numerical analyses of polarization-dependent optical gain saturations are given for quantum-well (QW) lasers in the presence of strain in the well regions in order to investigate the strain dependence of polarization-bistable operations. Gain saturation coefficients are obtained from nonlinear susceptibilities calculated in the perturbative analyses of density matrices. Band dispersions and dipole matrix elements, which are put into the density matrices, are calculated by diagonalizing Luttinger's Hamiltonian, including valence band mixing. The strain induces a change in band dispersions and wavefunctions, leading to strain-dependent saturation coefficients. The self-saturation coefficients and the cross-saturation coefficients (with orthogonal optical polarizations) pertinent to InGaAsP/InP QW vertical-cavity surface-emitting lasers are calculated. We find that the relative magnitudes of self- and cross-saturation coefficients are strongly dependent on the strain; in the presence of compressive strain, the cross-saturation coefficients are larger than the self-saturation in the wide range of the linear gain spectra, especially in the vicinity of the gain peak, indicating that the compressively strained structure is more favorable for the polarization-bistable operations.