An analysis of the stiffness theory reveals that coal mass compression bumps occur only when both the failure criterion and the stiffness criterion are simultaneously satisfied. Then a new structural factor called uneven stiffness coal seam structure (USCS) is proposed, which consists of an uneven stiffness coal seam along with continuous roof and floor. The USCS serves the dual functions of pressure concentration and stiffness reduction. The former facilitates stress concentration from the low stiffness zone (LSZ) to the high stiffness zone (HSZ), thus raising the risk (rF) of failure. The latter reduces the stiffness of the surrounding rock of the HSZ, allowing the system to meet the stiffness criterion even with a hard roof, thereby reconciling the contradiction between the stiffness theory and engineering experience and raising the risk (rI) of instability. The HSZ of the USCS, including thinning zones, bifurcating areas, magmatic intrusion areas, and remnant pillar affected areas, is more susceptible to coal bump incidents than a conventional coal seam. Mechanical analysis and simple numerical simulations validate the pressure concentration and stiffness reduction functions of the USCS. The results demonstrate the following: 1) The normal stress of the HSZ positively correlates with ER, HR, KH, and SL, but negatively correlates with KL and SH; The stiffness of surrounding rock of the HSZ negatively correlates with HR, KH, SL, and SH, but positively correlates with ER and KL. 2) Failures within the HSZ of the USCS enables the roof strata to release bending deformation energy without undergoing fracturing. 3) The alignment between the HSZ of an existing USCS and the HSZ of an artificial USCS advancing with the working face intensifies stress concentration and reduces stiffness, thereby significantly increases the risk (rCB) of coal bump. By applying the stiffness theory and relevant USCS findings, new explanations can be provided for engineering phenomena such as the time-delayed coal bumps, the inefficient pressure relief in ultra thick coal seams, and the “microseism deficiency” observed prior to certain coal bumps.