The magnetization behavior of soft magnetic thin-film elements is investigated in detail, based on a nanocrystalline iron-Permalloy multilayer system. Advantages of this material for domain analysis are a smooth surface and a good magneto-optical contrast due to a high saturation. Deviations from the mathematical model of an ideally soft magnetic two-dimensional film are due to the presence of anisotropy, to the actual structure of domain walls, and to edge anisotropies due to stress relaxation. These phenomena are observed for elements of various shapes. The effects of different anisotropies are studied by applying an external stress onto the thick ceramic substrate. Particular features connected with hysteresis, such as regular and anomalous corner configurations and the transitions between asymmetric Bloch and Néel walls are investigated.