Abstract: The mechanical model of first fracturing of main roof considering the support of coal pillars and solid coal as elastic foundation on both sides of stope is established. Using the differential algorithm and the fracture criterion of pri- mary moment,it is found that ① when the elastic foundation coefficient k is smaller as well as the thickness of main roof h and the elastic modulus E is larger, the initial fracture position of main roof is the lower surface of central region of hanging roof area on weaker coal pillar side. On the contrary,the position is the upper surface of long side area a- head of solid coal on weaker coal pillar side. ② When the support coefficients km1,km2 and the widths L1,L2 of coal pil- lars on the two sides of stope change,the primary moments and their positions ahead of coal wall in the central area of main roof and solid coal area are almost unchanged. However,the values and the positions of primary moments of main roof in coal pillars area on the two sides of stope change significantly. ③ When the thickness h and elastic modulus E of main roof are larger and the values of L1,km1,L2 and km2 are smaller,the main roof in coal pillars area on the two sides of stope will not fracture. So the fracturing order of the roof is that the lower surface of central region of hanging roof area on weaker coal pillar side → the upper surface of long-side solid coal area on weaker coal pillar side,and the final fracture form is the type of asymmetric “ = -X”. On the contrary,the main roof in coal pillars area on the two sides of stope will fracture. Thus the fracturing order is that the upper surface of long-side solid coal area on weaker coal pillar side → the lower surface of central region of hanging roof area on weaker coal pillar side → the upper sur- face of coal pillar area on stronger coal pillar side → the upper surface of coal pillar area on weaker coal pillar side, and the final fracture form is the type of asymmetric “O-X”. However,when L1,km1 are smaller and L2,km2 are larger, only on weaker coal pillar side,the main roof will not fracture,and the final fracture form is the type of asymmetric “U- X”. ④ When k,E and h change as well as km1 and km2 keep a certain arbitrary ratio constant with k,the ratio k / E or k / (Eh3 ) is unchangeable and the fracture law of main roof is invariant.