Abstract: Aiming at the support capacity at roof cutting during periodic weighting in mining of shallow coal seam, according to the nonlinear variation characteristics of immediate roof under unstable failure of abutment pressure, a systematic mechanical model composed of upper roof-immediate roof support-waste rock is established. The expressions for support compression quantities under the static and dynamic loading before and after the system instability are derived by using the correlation analysis methods of catastrophic theory and rock dynamics. The formula for calculation the support capacity at roof cutting is obtained and the main factors for the support capacity are analyzed. The results show that the unstable failure of immediate roof leads to the roof cutting. The jump value of the displacement of immediate roof rock directly determines the amount of dynamic loading. The support capacity relates to the cyclic weighting interval, upper load, thickness of immediate roof, stiffness ratio of immediate roof and support and material parameters when the system fails. The rationality of the theoretical derivation is verified by engineering example. The test results are of great significance to the support capacity at roof cutting and the selection of support types.