Magnetic Flux Leakage (MFL) sensing for in-line pipeline inspection of oil and gas pipes using pipeline inspection gages (PIG) based on permanent magnet magnetization is worldwide a well-known introduced non-destructive testing technique (NDT) by service companies to detect and size corrosion wall thinning due to id- and od-defects. However, the advantage - compared with other concurrent NDT techniques like for instance ultrasonic time-of-flight measurement - to be the cheapest-one is balanced by the disadvantage to depend on the locally achieved magnetization value. This value can scatter due to wall thickness changes along the length of a transportation line and magnetic coupling changes of the magnetizers to the pipe wall, especially in pipe bends producing a lot of amplitude scatter. Therefore it is of high interest of the pipeline pigging service industry to develop robust signal interpretation algorithms by which defect geometry influences can be imaged and visualized by use of less magnetic field-sensitive amplitude evaluation. Compared with experiments modeling is a much more flexible tool to vary quickly inspection parameter in order to learn its influence on inspection sensitivity and reliability. In the presented paper FE-approaches are discussed which scientifically are especially of interest as the pipes are ferromagnetic asking for modelling of the material's hysteresis behavior. The special emphasis of the paper is in defect reconstruction procedures and on the simulation of magnetization in the so-called "saturation branch" of the hysteresis.