Driving apparatus for imparting linear reciprocating movement to a shear on a flying shear apparatus or the like. A continuously constantly rotatable axle is provided with a pair of disks having cam surfaces on the periphery thereof engageable with guide rollers fixed at two lever arms of a three-armed lever, the third lever arm being connected to the flying shear by way of a coupling rod pivotably attached at the third lever arm and the flying shear. The cam disks are configured so as to impart motion to the shear in a feeding direction with a first feed segment of increasing velocity, a second feed segment of constant velocity, and a third feed segment of decreasing velocity, whereby the shearing operation can conveniently be executed during the phase of constant velocity. The cam surfaces are so constructed that motion of the shear in the return stroke direction includes a first return segment of increasing velocity and a second return segment of decreasing velocity, without the interposition of a constant velocity section.