Abstract: A fuel-injection pump of the distributor type has a distributor shaft which is coupled fixedly in terms of rotation to a drive shaft and which, during rotation, successively supplies an injection nozzle with fuel from a pump working space. Seated displaceably in each case in one of a plurality of radial bores in the distributor shaft are pump pistons which, on the one hand, limit the pump working space and, on the other hand, bear non-positively on a coaxial cam ring via rollers held in roller shoes. For a construction of the injection pump which is advantageous in manufacturing terms, the drive shaft engages over the distributor shaft by means of a cup-like coupling head, and a number corresponding to the number of radial bores, of axial slots for the displaceable reception of the roller shoes are made in the cup wall.