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In order to forecast peak cutting force of conical picks more accurately under conditions of plane cutting and symmetrical slotting，a new formula for calculating the peak cutting force and the formula which should satisfy the cutting boundary conditions are deduced theoretically. The derivation of the formulas were based on Evans' cutting model and assumed the stress distribution of conical surface of pick tip are different due to the clip effects of rocks when cutter cutting. Compared to other existing theoretical formulas，the calculation results are closer with the experimental value. In addition to considering the influence of some factors on the cutting force，such as half-cone angle θ of picks，tensile strength σt of rocks and friction coefficient f between picks and rocks，the brittleness index m of coal and rock is introduced. The formula should satisfy the cutting boundary condition which is represented by minimum limit of the ratio between cutting depth h and the vertical distance s from the loading position to the adjacent free border. That is smin/h，which mainly related to brittleness index m and almost unaffected by half-cone angle θ of picks. When m is 5 to 15，smin/h is between 2 and 3 and consistent with the existing experiments results. The derived formulas and conclusions can provide theoretical basis and guidance for the further analyzing and deducing of real peak cutting force containing more parameters of conical picks under actual mining condition. [ABSTRACT FROM AUTHOR]