An inexpensive type of linear solenoid actuator for moving a plunger along a straight line, while providing a force on the plunger due to the actuator which does not vary greatly over the length of stroke of the plunger; a spring opposes the force exerted on the plunger by the solenoid, so that the plunger will assume any of a range of positions in response to different currents through the solenoid. The plunger has a first larger portion of magnetic material sliding in a first bearing; a tapered second magnetic portion extending forwardly from the first portion; a magnetic third portion of substantially cylindrical form extending forwardly from the tapered portion; and a front non-magnetic portion sliding in a second bearing and supporting the front end of the plunger. The second bearing is in a magnetic end piece having substantial axial width. The stroke of the plunger is preferably such that the forward end of the magnetic third portion moves from a first position near the adjacent end of a magnetic end piece in which the second bearing is mounted, to a second position well within or outside the other end of the magnetic end piece.