This invention relates to an apparatus and method for producing a flexible sheet material having a predetermined surface characteristic of high quality and definition formed on one side thereof. The apparatus of this invention comprises first and second rotating rolls which are mounted on a generally horizontally extending axis with the peripheral surfaces thereof closely spaced from one another to form a narrow gap corresponding to the desired overall thickness of the composite sheet. The second rotating roll has a peripheral surface of a predetermined texture corresponding to the desired surface characteristic to be produced in the sheet. A base web of predetermined thickness less than the narrow gap is directed onto the peripheral surface of the first roll and is advanced along an arcuate path around the periphery of the first roll and then through the narrow gap between the first and second rolls. The base web, upon passing through the narrow gap, is then directed around the second roll and along a predetermined arcuate path around the periphery thereof. A flowable uncured actinic radiation curable thermosetting resin is directed behind the narrow gap between the first and second rolls and into contact with the exposed surface of the base web so that a coating of the resin is applied to the base web and is carried with the base web through the narrow gap to this position the coating, upon emerging from the gap, beneath the base web and in contact with the peripheral surface of the second roll. Then actinic radiation is directed through the base web and onto the coating to cure and harden the coating while in contact with the pattenered surface of the second roll. The base web is then directed away from the second roll to separate the cured and hardened coating from the roll and thus produce a sheet with a predetermined surface characteristic of high quality and fine definition accurately reproducing the surface texture of the second roll.