Abstract: The researches on sloshing of the free surface flow in containerscarrying liquid are of theoretical and practical significance. Numericalsolutions often involve some approximations of the boundarycondition, when considering the wide-range movement or the nonlinearityof the free surface flow. In this paper, under partial slip boundary conditions,the high-order nonlinear differential equations of a cylinder-shapedpartially filled liquid container are numerically solved. Theinfluences of the contact line and the fluid height of liquid and the partial slipboundary conditions on the macroscopic radius of the fluid layer are discussed. The results may serve a reference for treating similar boundaryconditions of free surface flow for partially filled liquid carryingcontainers.