The 3-D traction field in the pressure screw-pair of a 3 500 heavy and medium plate mill press down system is successfully calculated by applying the 3-D frictional contact multipole-BEM and the corresponding program that has been developed. The computing results show the medium diameter orientation is unreliable, especially under the interference of an outer force couple. Under such working conditions, the circumferential traction distribution on the screw teeth is extremely uneven, which is the main reason for the destruction and short life time of screw-pairs. When utilizing the same precision (the relative tolerance is 10× 10-5), the multipole-BEM uses almost the same CPU time as used by the FEM, but the needed computer memory size is only one eightieth of that needed by the FEM (10 MB vs. 800 MB). The multipole-BEM is well suited for computing large-scale engineering problems. The 3-D traction field in the pressure screw-pair of a 3 500 heavy and medium plate mill press down system is successfully calculated by applying the 3-D frictional contact multipole-BEM and the corresponding program that has been developed. The computing results show the medium diameter orientation is unreliable, especially under the interference of an outer force couple, especially under the interference of an outer force couple, especially under the interference of an outer force couple, especially under the interference of an outer force couple. When utilizing the same precision (the relative tolerance is 10 × 10-5), the multipole-BEM uses almost the same CPU time as used by the FEM, but the needed computer memory size is only one eightieth of that needed by the FEM (10 MB vs. 800 MB). The multipole-BEM is well suited for computing large-scale engineering problems.