A theory of polaritonic states is developed for a nanostructure with a wide quantum well stressed perpendicular to the growth axis of the heterostructure. The role of the $K$-linear terms appearing in the exciton Hamiltonian under the stress is discu
ssed. Exciton reflectance spectra are theoretically modeled for the nanostructure. It is predicted that the spectral oscillations caused by interference of the exciton-like and photon-like polariton modes disappear with the increase of applied pressure and then appear again with opposite phase relative to that observed at low pressure. Effects of gyrotropy and convergence of masses of excitons with heavy and light holes due to their mixing by the deformation is also considered. Numerical estimates performed for the GaAs wells show that these effects can be experimentally observed at pressure $P < 1$~GPa for the well widths of a fraction of micron.
