Si, Ge, and GaAs have been extensively investigated as alternative substrates for molecular-beam epitaxy (MBE) growth of HgCdTe and, at present, are widely used for HgCdTe-based infrared focal-plane arrays. However, the problem of high dislocation density in HgCdTe layers grown on these lattice-mismatched substrates has yet to be resolved. In this work, we investigated another alternative substrate, GaSb, which has a significantly smaller lattice mismatch with HgCdTe in comparison with Si, Ge, and GaAs, and is readily available as large-area, epiready wafers at much lower cost in comparison with lattice-matched CdZnTe substrates. The resultant stress due to lattice and thermal mismatch between the HgCdTe epilayer and various substrates has been calculated in this work using the elasticity matrix, and the corresponding stress distribution simulated using ANSYS. The simulated structures were matched by experimental samples involving MBE growth of HgCdTe on GaAs, GaSb, and CdZnTe substrates, and were characterized via reflection high-energy electron diffraction and x-ray diffraction analysis, followed by etch pit density (EPD) analysis. In comparison with other alternative substrates, GaSb is shown to have lower interface stress and lower EPD, rendering it an interesting and promising alternative substrate material for HgCdTe epitaxy.