The movement of overburden rock in coal mine goafs, caused by oil and gas drilling disturbances and the gravity of overlying rock strata, affects drilling and completion operations as well as casing safety. The Jiaojiagou goaf was taken as an example, a differential meshing strategy was adopted and three-dimensional finite difference analysis model of the goaf was established to simulate the actual conditions. Based on the Mohr-Coulomb failure criterion, numerical simulations were conducted using FLAC^3D to analyze the displacement and stress variation patterns of overburden rock under room-and-pillar, strip, and caving mining goafs, comparing the differences between the numerical simulation results and the measured data for the room-and-pillar goaf. The results show that as the mining distance increases, the maximum vertical displacement in the caving type is 9.40 and 7.24 times that of the room-and-pillar type and strip mining type, respectively, demonstrating bigger damage severity. The caving mining goafs should be avoided in oil and gas drilling location. The maximum vertical compressive stress in the caving type is 25.20% and 24.57% higher than that in the room-and-pillar type and the strip mining type, respectively, making it more susceptible to collapse. As the mining distance increases, the maximum displacement under the caving type is about 8 and 7 times greater than those of the room-and-pillar and strip types, while the trends of maximum vertical and horizontal surface displacements are basically consistent. Compared with field-measured data, the model's relative error is approximately 5%. A new method is provided by this study for predicting overburden displacement and stress in coal mine goafs. The findings can be used as a reference for drilling and completion design in coal mine goafs, especially for the casing program design and safety analysis.