Abstract: There are various forms of multilateral horizontal wells for developing coalbed methane, and the role of cleats in the development process is unclear. It is necessary to investigate the impact of the discrete cleat distribution in coal seams and the multilateral horizontal well configuration on gas well productivity. Based on the density and orthogonal characteristics of face and butt cleats in coal seams, the low density, medium density, and high density discrete cleat systems in coal seams are constructed using random methods. Combined with four different forms of multilateral horizontal wells, namely equal-length type, spindle type, staggered type, and dumbbell type, a physical model for developing coalbed methane using multilateral horizontal wells is constructed. The stress sensitive model of coal matrix and cleat system is established considering the effective stress change of coal seams and the matrix shrinkage effect in the development process. The desorption of coal-bed methane is calculated using Langmuir theorem, and a development model of compressible coal-bed methane flowing in the coupling of coal matrix, cleat system and multi branch horizontal wells is established. Furthermore, the influence of the cleat density and the configuration of multilateral horizontal wells on the development of coal-bed methane is studied. The results show that the discrete cleats in coal seams can greatly increase the drainage area of multilateral horizontal wells in a short period of development time, but are only limited to the cleats directly connected to multilateral horizontal wells and surrounding matrix areas. The parts that are not connected to multilateral horizontal wells require longer development time, which is also an important reason for gas wells to achieve peak production in a short period of time and quickly reduce production. The drainage area controlled by equal-length multilateral horizontal wells is the largest, while the drainage area of staggered type, dumbbell type, and spindle type decreases sequentially. When the cleat density is the same in the coal seams, the daily peak production and cumulative production within 20 years of the equal-length multilateral horizontal wells are higher than those of the other three types of multilateral horizontal wells, which can achieve better development results. By increasing the angle between the main and secondary wellbore of multilateral horizontal wells, the development effect of equal-length multilateral horizontal wells becomes much better, and the peak daily production of spindle multilateral horizontal wells is significantly improved. The peak daily production of staggered and dumbbell multilateral horizontal wells is more sensitive to the number of branches. The number of branches in spindle multilateral horizontal wells should not be less than eight, while the number of branches in the dumbbell multilateral wells should not be more than six.