The invention relates to a cover plate structure of a flexible display module, the flexible display module and flexible display equipment. The cover plate structure of the flexible display module comprises an organic cover plate layer and a flexible glass layer which are attached to each other, the flexible glass layer is provided with a first part and a second part, the first part is located in an area, corresponding to a bendable area of the flexible display module, on the cover plate structure, and the second part is located in an area, corresponding to a non-bending area of the flexible display module, on the cover plate structure; the first part of the flexible glass layer is thicker than the second part; or the flexible glass layer is only arranged in the area, corresponding to the non-bending area of the flexible display module, of the cover plate structure. According to the scheme, the overall resilience force of the flexible display module can be reduced when the flexible display module is bent, and attachment between the layers of structures can be better maintained. In addition, the dislocation amount of the edge of the supporting layer when the flexible display module is bent can be reduced, and therefore the probability that a Pad bending area of the flexible display module is damaged in a jacking mode is reduced.