Abstract Based on the characteristic of deep rock layers and the theory of key strata, we analysed elastic mechanical characteristics of key strata by using elastic plate theory. The results show that the deformation and distribution of internal forces of key strata vary with different mine boundary conditions. The boundary values of key strata with three point boundaries and one fixed boundary is greater than that with four fixed boundaries. Considering the rheology of key strata under low stress conditions, we selected a generalized Kelvin model to analyse the rheology characteristics of the key strata and discovered their instantaneous elastic phases. The rate of deformation decreased over time to the point where the key strata reached stability. But over this time, the effect on deformation became very clear. For high stress conditions, we chose a Burgers model and found deformation of key strata in the form of attenuation and steady-state creep and although the rate of deformation remained constant, secondary creep was obvious, causing instability in the system. As well, we analysed the effect of creep buckling and derived a relation between buckling force and time.