A reversible flow pump (12) comprising: a first port (16) and a second port (20); a rotor (60) comprising a plurality of pump elements (74-80) movable through a fill mode and a discharge mode, a pump chamber (140) associated with each pump element (74) which are respectively filled and discharged; a ported shaft (30) rotatable between a first position and a second position, for carrying fluid to and from the various pump chambers (140), such that when in the first position fluid received at the first port (16) is communicated to fill each pump chamber (140) during the fill mode, at least a portion of such fluid is discharged therefrom and communicated to the second port (20), and wherein in the second position fluid flow is reversed. A brake system incorporating the pump is also disclosed.