A vane pump (10) including a cylindrical rotor (78) rotatable inside of an oval-shaped rotor chamber (66) defined by a cam ring (46) round the rotor. A thrust plate (42) and a pressure plate (44) on opposite sides of the cam ring cover the rotor chamber (70) and are squeezed together by a pressure force attributable to fluid in a discharge chamber of the vane pump at a discharge pressure thereof. Fluid at the discharge pressure of the pump is ported to an annular first longitudinal balance chamber (116) between the pressure plate (44) and an end (82A) of the rotor facing the pressure plate (44) and to an annular second longitudinal balance chamber (118) between the thrust plate (42) and an opposite end (82B) of the rotor facing the thrust plate. A pressure force on the pressure plate (44) attributable to fluid in the first balance chamber (116) balances a fraction of the pressure force on the pressure plate attributable to fluid in the discharge chamber to reduce flexure of the pressure plate into the rotor chamber. A pressure force on the rotor attributable to fluid in the second balance chamber (118) is equal to the pressure force on the rotor attributable to fluid in the first balance chamber (116) for longitudinal static equilibrium.