The mechanical characteristics of materials are described by appropriate mathematical models as a basic technique for the manipulation of their corresponding virtual objects. In this study, virtual objects are assumed to consist of combinations of viscoelastic elements. Their dynamic characteristics are given within and beyond the range of elastic limitation of the edges of the elements by the calculation of their discrete-time models. Then, a sheet-type virtual solid object with various physical properties is theoretically cut by knives where their cutting mechanism is analyzed under some assumption. The resistance moment to the grips of knives on their cutting of synthesized material is confirmed similar to the actual one on the cutting of its corresponding actual material.