Cylinders, tubes, cuboids, etc. are basic magnet shapes used in permanent magnet machines. The relative positions between magnets include parallel, perpendicular, or inclined. The force and torque between two cuboid
magnets of almost any status and two cylindrical magnets with paralleled axes have been solved. Using the theory of magnetic charges and magnetic Coulomb’s law, this study derives a mathematical model for interaction forces and torques between two perpendicular magnetic tubes in three dimensions. Using this model, the effects of tube relative positions on the interaction forces and torques is analyzed by numerical calculation. The model can also express interaction forces and torques between a magnetic tube and magnetic cylinder or between two magnetic cylinders when the inner radius of one magnetic tube is zero or the radii of both tubes are zero. This study provides the theoretical background for magnetic tube and cylinder applications, such as magnetic drive or control across space in mechanical, medical treatment, chemical industry, food production, aerospace, etc.