The computer simulation is presented of gravure ink transferring behavior and penetration to the paper when an gravure roller is used to transfer a printing ink onto a substrate. The three dimensional unsteady ink motion is simulated by Polyflow package software and experimented by IGT gravure printing test machine. The simulation is performed where the flow domain is bounded above by a stress free surface and bounded below by a moving substrate. Specific predictions are made for particular pattern of cells and substrates. Cell size and ink rheological properties are found to be the principal determination of transferring behavior. Simulation is currently restricted to the flow domain beneath the receding meniscus. Both Newtonian and shear thinning inks are considered.