The transport of methane molecules into several open-ended carbon nanotubes is studied with classical, nonequilibrium molecular dynamics simulations. The forces in the simulations are determined using a reactive empirical bond order potential for short-ranged interactions and a Lennard-Jones potential for long-range interactions. The simulations show that until the carbon nanotubes are filled with methane molecules up to a specific cutoff molecular density, the molecules move forward and backward along the axis of nanotubes in a “bouncing” motion. This bouncing motion is observed for molecules inside both hydrogen-terminated and non-hydrogen-terminated opened nanotubes and is caused by a conflict between the molecules’ attractive interactions with the interior of the nanotube and their response to the molecular density gradient down the length of the tube. At molecular densities above the cutoff value, the molecules flow into, through, and out of the nanotubes in a linear manner. The effects of molecular density, nanotube diameter, and nanotube helical symmetry on the results are analyzed.