Aiming at the problems of unclear load transfer mechanism of overburden rock under the influence of mining and difficult to quantitatively characterise the lateral support pressure distribution, this paper establishes a hypothetical cantilever beam mechanical model of elastic foundation based on the assumption of Winkler's elastic foundation according to the spatial structural characteristics of the peripheral rock of the quarry after the coal seam mining, and adopts the Rayleigh-Ritz method to derive the distribution equations of the lateral support pressure on the coal body under the action of the overburden rock's centralised load in the mining area, and verifies the theoretical model by numerical simulation in the context of actual engineering. The theoretical model was validated by numerical simulation with the background of actual engineering. Through the model verification and parameter analysis, the results show that: (1) the support coefficient c in the model parameters does not affect the support pressure value, but has a greater impact on the vertical displacement of the lateral coal body, and the vertical displacement decreases with the increase of the support coefficient c. The support pressure value is mainly related to the mining influence range l and the value of mining overburden load F, in which the mining overburden load F and the depth of the coal seam are positively correlated, and the deeper the depth of the coal seam is, the higher the support pressure value increases, and the mining influence range l increases, and the mining influence range F increases, and the mining influence range l increases. The larger the burial depth is, the value of bearing pressure increases, and the value of mining influence range l mainly affects the distribution of bearing pressure; (2) the field measurement and numerical simulation show that the mechanical model calculation results and the measured data in the elastic deformation zone are highly consistent, indicating that the model established in this paper can better reflect the vertical deformation of the lateral coal body under the action of overburden load in the mining hollow zone, as well as its distribution of the bearing pressure within the elastic deformation range. This paper provides a theoretical basis for the study of overburden load transfer and working face peripheral rock deformation under the influence of mining, which is of great significance in guiding the safe mining in the mining area