To prevent a vane pump from being overloaded without using any relief valve.

A ring groove 21c extending outward in the radial direction is formed in a side plate 31R confronting a vane push-up port 37b formed in the side face of the rotor 37R of this vane pump, and thereby a flexible part 21d having a small wall thickness is formed easily deflecting outward in the axial direction. When the vane pump rotates at a high speed and its discharge pressure exceeds the specified level, the flexible part 21d is deflected in the direction of separating from the rotor 37R by the pressure acting on the port 37b, and there a gap α is formed. As a result, the working oil in the port 37b is released to a low pressure part upon passing through the gap α, so that any relief valve otherwise required in a conventional arrangement can be eliminated to allow a decrease of the number of component parts and a small and light construction of the vane pump, and also the vane pump is precluded from acting of an excessive load to lead to enhancement of its durability.