The deflection of cutting wire on multi-wire saw is determined by cutting wire tension, diameter ingot feed force and some other factors, and it affects the quality of silicon wafers greatly. In this paper, the initial stage of cutting process is analyzed and modeled with three ODEs. Then the numerical solutions are solved by finding out the BVPs of each ODE. The numerical solutions showed the relationship between the deflection and the cutting parameters such as cutting wire tension, diameter and ingot feed force. This method is helpful for the further research of modeling the entire cutting process.