A theory of polaritonics tates is developed for a nanostructure with a wide quantum wells tressed perpendicular to the growth axis of the heterostructure. The r ole of the K-linear terms appearing in the exciton Hamiltonian under the stress is discussed. Exciton reflectance spectra are theoretically modeled f or the nanostructure. It is predicted t hat t he spectral oscillations caused by interference of the excitonlike and photon-like polariton modes disappear with the increase of applied pressure and t hen appear again with the 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 are 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 a micron.