A work roll crossing type rolling mill has back-up rolls arranged in such a manner that their axes are not inclined in a horizontal plane. Work rolls are constructed in such a manner that their axes can be inclined in a horizontal plane relative to the backup rolls such that the axes of the work rolls cross the axes of the back-up rolls and such that the axes of the work rolls cross each other. A lubricant supply device is provided for supplying a lubricant between each work roll and each back-up roll combination to greatly reduce the thrust exerted to the work rolls, whereby the rolling mill is given an excellent ability of controlling the crown of the material to be rolled.