Most prediction methods used to calculate mining-induced subsidence are empirical, which cannot explain the mechanism of fundamental rock strata movement. In this paper, based on key stratum theory and the mechanical analysis of overburden, a new analytical solution, the Analogous Hyperbola Subsidence Model (AHSM), was proposed to describe the movement and damage of inner burden. Mining-induced rock strata movement was verified using the Distinct Element Method (UDEC), to assess the performance of the theoretical model. Three subsidence parameters (Smax/T, Sgoaf/Smax, D/H), generally used to describe surface subsidence trough, agree with statistical field measurements of the South Coalfield in Australia. The surface subsidence and the movement boundary in the overburden are very close to the theoretical predictions. Additionally, the primary key stratum damages the least in the overlying strata: its broken length is the smallest. The width of subsidence trough and maximum surface subsidence increase as the primary key stratum drops.