The magnetization behavior and thus the form of the magnetization curve of electrical steel strongly depend on the direction of the magnetic field, frequency of excitation, external mechanical stress, and cut edge effect. These factors influence the performance of electrical machines and need to be considered in advanced machine design processes or numerical modeling. Most of the aforementioned effects occur locally in the machine and, therefore, need to be described locally. It is crucial to characterize the material under realistic conditions for adequate identification and quantification of the influences. In this article, modeling and simulation of soft magnetic material are performed based on a detailed magnetic characterization, considering magnetization amplitude, angle with respect to the rolling direction of magnetization, mechanical stress, and cut edge effect. The dependent soft magnetic material characteristics are derived from the magnetic measurement data and concluded into interpolation surfaces. Subsequently, these surfaces are used to simulate a synchronous machine designed for a traction drive of an electric vehicle by finite-element simulation. One of the main challenges is the correct determination of the local material properties, depending on the operating point, which influences global quantities such as losses and torque. This article provides a methodology to consider different local influences on the magnetization behavior of electrical steel in a finite-element simulation, thus offering the potential for improving electromagnetic circuit design.