We find the deformation and stresses occurring in an infinite rod of a magnetizable material with square normal cross-section, subjected to an external, transversal and initially uniform magnetic field of arbitrary direction. The numerical solution of the uncoupled problem is obtained using a boundary integral method. This yields the boundary values of all the unknown functions of the problem. The results are discussed in detail. Applications concern the calculation of stresses in straight portions of elastic, magnetizable cylinders subjected to transversal magnetic fields.