Based on the contact constraint method and LuGre friction model, the dynamic problem of oblique impact with friction between a flexible beam system and a slope is studied. The rigid-flexible coupling multi-body system dynamics theory is used to discretize and model the flexible beam with large overall motion, at the beginning of the impact, the impulse-momentum method is used to calculate the jumping velocity, and then the contact constraint is introduced in the normal direction to solve the impact force, in tangential direction, LuGre friction model is used to solve the friction force in two ways, the first is that the friction force is calculated by friction coefficient and collision force when sliding, and introducing tangential constraint to calculate Lagrange multiplier response actual friction force, according to the stick / slip switching judgment, the friction force in the impact process is calculated (which is consistent with that calculated by Coulomb friction model); the second method is to calculate the friction force according to friction coefficient of LuGre friction model and normal collision force, so there is no need to switch between stick and slip during impact, and the same friction calculation formula is used. Compared with Coulomb friction model, LuGre friction model is more accurate in describing the tangential friction process. There is no difference between the two LuGre friction model modeling methods to describe the impact dynamics. Therefore, it shows that the establishment of normal contact constraint and LuGre friction model can meet the collision un-embedding situation to avoid stick slip switching and to describe the relatively accurate advantages of friction.