Differences in the thermal expansion of a thin GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As multiple-quantum-well (MQW) sample and a thick sample holder to which it is fixed, lead, by varying the temperature, to a homogeneous biaxial strain in the MQW sample. It can be decomposed into a hydrostatic and a uniaxial component. Using different sample holders the stress can be made tensile (quartz) or compressive (${\mathrm{BaF}}_{2}$). In the temperature range between 300 and 20 K we observe in optical transmission the corresponding shift and changing splitting of the exciton lines formed with heavy and light holes. The experimental data are well described by subband calculations based on an 8\ifmmode\times\else\texttimes\fi{}8 k\ensuremath{\cdot}p model, which includes the dependence of the band-edge energies on temperature and stress.