Abstract: Based on the anisotropy of permeability of coal and rock and the difference of horizontal principal stress, and the phenomenon that the velocity of horizontal fracture is different in each direction, the axial length ratio is proposed to control the velocity of horizontal fracture in each direction, and a calculation method of axial length ratio is given. On the basis of Penny model, the mathematical model of horizontal joint extension in Non-Newtonian fluid is established, and the display formats of joint length, maximum width and pressure drop are given. The influences of axis length ratio, construction pump rate, fracturing fluid viscosity and comprehensive filtration coefficient on the calculation results are analyzed by numerical calculation and single factor variable method. The results show that increasing the viscosity of fracturing fluid can greatly increase the width of horizontal fracture. After increasing pump rate, radial seam length and width both increased to some extent. When the filtration loss increases, the three-dimensional size of cracks decreases, and the width of cracks decreases rapidly. The calculation formula of axial length ratio and the establishment of non-equal diameter expansion model provide a new method for the calculation and mechanism analysis of horizontal joint size.