Abstract: In order to describe top coal caving shapes, the broken top coal was regarded as random flowing loose medium.By using PFC2 d software, the two-dime nsional model in transverse section was established, and the shapes of caving top coal could be worked out through discrete element iteration method.Based on the bo undary spherule coordinate, the two-dimensional function of caving top coal was determined by carrying on data ftting to the two-dimensional equation of random medi um theory.The top coal caving was a three-dimensional process. The paper assumed that the process of top coal caving were mutual independent in transverse section and longitudinal section, according to the boundary spherule coordinate, the three-dimensional equation of drawn top coal could be determined by data fitting to the thr ee-dimensional equation of random medium theory.It presented that the random medium theory was feasible to top coal caving study for the function image and the sim ulated drawn top coal shapes being basically identical.It could determine rationally coal caving parameters during production process.