Abstract: A slender rod string in a vertical cylinder is subjected to an alternating tension-compression axial load. When the axial pressure at the bottom of the rod is greater than the buckling critical load, in the slender rod, a helical buckling deformation will be generated, and the transverse vibration of the rod will be stimulated by the buckling deformation. Taking the instantaneous buckling configuration of the slender rod in the cylinder as the displacement excitation of the transverse vibration, a simulation model for the collision between the slender rod and the inner wall of the cylinder under the instantaneous buckling displacement excitation is established. To solve the mathematical problem, the finite difference method is used to discretize the rod, and the Newmark method is used to discretize the time. The transverse vibration mathematical model is implemented in the numerical simulation, with the collision conditions between the slender rod and the cylinder satisfied by the method of the restitution coefficient. It is shown that the collision occurs mainly after the rod string is buckled, and the collision almost occurs along the whole cylinder with the collision force increasing gradually from the top of the cylinder to the bottom. But when the bottom load is a tensile force, few collision occurs and the collision force is also very small.