An engine assembly having an engine, an engine cover and a vane pump, said vane pump including: a housing that has a tubular peripheral wall portion and a bottom wall portion which is disposed at one end of the peripheral wall portion in an axial direction and in which a discharge hole is provided to open, and that defines a pump chamber communicating with the discharge hole inside the housing; a rotor that is disposed in the pump chamber and that is rotatable about a rotational axis of the rotor; a vane disposed so as to be slidable with respect to the rotor in a radial direction, the vane partitioning the pump chamber into a plurality of working chambers (A1, A2) and causing capacities of the working chambers (A1, A2) to increase and decrease along with rotation of the rotor; and a reed valve that opens and closes the discharge hole to allow a compressible fluid compressed in the working chambers (A1, A2) and an incompressible fluid to be discharged intermittently, a position at which a sliding direction of the vane with respect to the rotor is inverted from outward in the radial direction to inward in the radial direction during forward rotation of the rotor is defined as a reference position (θ1); a section of the pump chamber on a side of the discharge hole with respect to the reference position (θ1) is defined as a discharge section; a pressure relief groove is disposed in a portion of an inner surface of the bottom wall portion corresponding to the discharge section with a clearance secured between an inner surface of the peripheral wall portion and the pressure relief groove; and a pair of the working chambers (A1, A2) on both sides of the vane in a rotational direction communicate with each other via the pressure relief groove when the vane overlaps the pressure relief groove during forward rotation of the rotor, characterized in that the pressure relief groove extends between both sides in the rotational direction with reference to a position directly below the rotational axis. a housing that has a tubular peripheral wall portion and a bottom wall portion which is disposed at one end of the peripheral wall portion in an axial direction and in which a discharge hole is provided to open, and that defines a pump chamber communicating with the discharge hole inside the housing; a rotor that is disposed in the pump chamber and that is rotatable about a rotational axis of the rotor; a vane disposed so as to be slidable with respect to the rotor in a radial direction, the vane partitioning the pump chamber into a plurality of working chambers (A1, A2) and causing capacities of the working chambers (A1, A2) to increase and decrease along with rotation of the rotor; and a reed valve that opens and closes the discharge hole to allow a compressible fluid compressed in the working chambers (A1, A2) and an incompressible fluid to be discharged intermittently, a position at which a sliding direction of the vane with respect to the rotor is inverted from outward in the radial direction to inward in the radial direction during forward rotation of the rotor is defined as a reference position (θ1); a section of the pump chamber on a side of the discharge hole with respect to the reference position (θ1) is defined as a discharge section; a pressure relief groove is disposed in a portion of an inner surface of the bottom wall portion corresponding to the discharge section with a clearance secured between an inner surface of the peripheral wall portion and the pressure relief groove; and a pair of the working chambers (A1, A2) on both sides of the vane in a rotational direction communicate with each other via the pressure relief groove when the vane overlaps the pressure relief groove during forward rotation of the rotor, characterized in that the pressure relief groove extends between both sides in the rotational direction with reference to a position directly below the rotational axis.