In this paper, we present the formulation of the stress distribution within a viscoelastic material subjected to distributed pressure on the free surface. In the formulation, the stress tensor at any point in the material is obtained with two steps. First, the elastic-viscoelastic correspondence principle is applied to obtain the stress solution for viscoelastic materials under a point load. Second, the obtained solutions from first step are integrated over the stress-applying area. Based on the formulation, the tress tensor at any point in the material is calculated numerically. This formulation can be used to simulate many practical contacting problems; one important example is the biomaterial cutting operations where a blade interacts with a biomaterial. In cutting, the effect of slicing angle on the stress distribution is an important factor to be included in the discussion. The slicing angle is determined by the magnitudes of tangential and normal components of the cutting force. Using the calculated principal stresses, it is possible to predict the location of damage using failure criterion such as Tresca's criterion. The results can serve as guidelines for several applications where the stress distribution and fracture prediction in viscoelastic materials are concerned.