A high pressure pump for decreasing an initial axial force of a clamping bolt and preventing distortion of a sealing surface and a cylinder form. The high pressure pump has an intermediate member including a cylinder body. The cylinder body has a pressurizing chamber communicated with a cylinder accommodating a plunger. Fluid in the pressurizing chamber is pressurized by reciprocating the plunger. The intermediate member is arranged between a cover and a flange and clamped by a clamping bolt. The clamping bolt has an exposed area at its axially central area where the entire periphery of the clamping bolt is exposed from the cover and the flange. One or both of the cover and the flange clamp the intermediate member with a flexing elastic force.