An arrangement for supporting a shaft of a vacuum pump includes a first bearing for supporting the shaft at one of its end, a second bearing for supporting the shaft at another of its ends and formed as a rolling bearing, a holder for receiving the second bearing and including an oscillating base, a fixation member secured in the vacuum pump housing, metallic connection members for connecting the oscillating base with the fixation member and axial springs arranged between the oscillating base and the fixation member and providing for the axial stiffness of the holder which is greater than its radial stiffness thereof and greater than the axial stiffness of the first bearing.