Bio-material cutting, such as meat deboning, is one the most common operations in food processing. Automating this process using robotic devices with closed-loop force control has shown some promise. The control of the force trajectory directly relates to the internal stress in the material being cut, and must provide enough force to initiate the cut. The ability to model the stress distribution in the bio-materials being cut would provide a better understanding of the influencing factors and help predict the required cutting force for the design of the cutting mechanism and for automating the cutting operations. This research is presented in two parts: part I models the stress distribution when a blade acts on the bio-material and part II discusses the principles of biomaterial cutting. Starting with modeling a point force in the normal and tangential direction on the boundary of a semi-infinite body, an analytical expression for the stress tensor has been obtained and simulated using direct integral method. This paper provides the theoretical basis for explaining the cutting phenomena and predicting the cutting forces, a topic to be presented in Part II.