To control methane emissions in gob into longwall working faces, it is necessary to understand the distributions of methane enrichment zones (MEZ) around mined coal seams with different incidence angles. In this paper, FLAC3D software is used to calculate the three-dimensional stress distributions in MEZ in gobs with coalbed incidence angles ranging from 0° to 50°. The results show that MEZ consistently exhibit a "hexagon" shape, and rotate in a clockwise direction as the coalbed angle increases. The MEZ range above the mined seam is larger than that below the mined seam. As the coalbed angle increases, the MEZ range in the roof decreases, while the MEZ range in the floor increases. The MEZ height increases significantly as the coalbed angle increases. The MEZ widths in coal pillars of gobs increase slightly as the coalbed angle increases. The methane concentration increases exponentially as the height in the MEZ increases. The surface borehole bottoms located relatively higher in the MEZ can drain methane with a higher concentration and flow rate, as verified by a field test in the Pansan mine, China.