The improved transporting apparatus for scanning exposure of a recording material as it is fixed on an exposure mount which is moved by means of a screw transmission mechanism is characterized in that the exposure mount for transporting the recording material is composed of a platen for carrying the recording material and a transport plate that holds the platen and which engages the screw transmission mechanism, with the platen and the transport plate being designed to be capable of relative displacement by small amounts, preferably in a non-contact relationship. Optionally, urging members may be provided to combine with the platen and the transport plate to form a vibration system that composes a vibration filter. The apparatus effectively absorbs not only vibrations that originate from the drive system to be transmitted to the exposure mount via the travelling nut of the screw transmission mechanism, as exemplified by erratic rotation or vibrations of the motor and the screw shaft of the screw transmission mechanism, but also vibrations due to externally applied forces and, hence, highly precise scanned transport of the recording material can be accomplished while suffering from very small levels of unevenness in the speed of its transport that will occur on account of those unwanted vibrations.