A quasistatic and steady state contact problems of paper nipped in rubber rollers was analyzed by using a stress function in the form of series. The model was derived from paper feed unit of duplicating machine. The point interpolation meshfree method (PIM) and the Schmidt method were applied to obtain the solution of the dual series equations. Stress distribution and surface speed ratio of the rubber rollers and paper were obtained based on elasticity theory. The purpose was to provide reference for improving the reliability of rubber roller of duplicating machine.