  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 discussed. 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.
