Solid backfill mining (SBM) is a form of green mining, the core of which is to control and minimize the deformation and movement of strata above longwall coal mines. Establishing a mechanical model that can reliably describe roof deformation by considering the viscoelastic properties of waste gangue is important as it assists in improving mine designs and reducing the environmental impact on the surface. In this paper, the time-dependent deformation characteristics of gangue under different stress levels were obtained by using lateral confinement compression, that reliably represents the compaction of goaf. The viscoelastic foundation model for gangue mechanical response is different from the traditionally used elastic foundation model, as it considers the time factor and viscoelasticity. A mechanical model using a thin plate on a fractional viscoelastic foundation was established, and the roof deflection, bending moment, time-dependent, viscous and other characteristics of SBM were included and analyzed. Compared with the existing elastic foundation model, the proposed fractional order viscoelastic founda-tion model has higher accuracy with laboratory data. The plate deflection increases by 50.9％ and the bending moment increases by 37.9％after 100 days, which the elastic model would not have been able to predict.