Combining with basic phenomenon in rock fracturing by external load, the analysis is made on the process of crushing rock by rotary drilling to get the helical breaking form. Based on the conditions of pressing into the rocks and selecting a single cutting pick as calculation model, the theoretical formula of axial pressure is obtained; then with the reference of Coulomb-Navier internal friction theory, the theoretical calculation formula of cutting force is obtained. According to different types of drilling tool, the calculation formula of single cutting teeth is extended, the formulas for calculating the pressure and torque parameters of rotary drilling rig are obtained. The influence factors under specific conditions in the axial force and cutting force calculation formulas are simplified, the theoretical relationship between drilling penetration rate and cutting force in rotary drilling process is obtained. Finally, by dynamic analysis software LS-DYNA, change curve of cutting force of single pick in different drilled depth is simulated, and the comparison is made on the simulated curve and the theoretical calculated curve under the same condition to get the theoretical calculation formula for cracking parameters of single pick, which can be reference for the design of rotary drilling rig.