AbstractWe describe a sequential addition and migration (SAM) algorithm for generating microstructures of fiber‐reinforced composites with a direct control of the magnitude of curvature of the fibers. The algorithm permits to generate microstructures with fibers that are significantly longer than the edge lengths of the underlying cell. Industrially processed short and long‐fiber composites naturally feature a high volume fraction, which needs to be reflected by state‐of‐the‐art microstructure generation tools. Nowadays, it is well understood that digital twins of the microstructure of composites are essential for reliable computational multiscale methods. The original SAM algorithm was shown to reliably generate microstructures for short and straight cylindrical fibers. Digital volume images reveal, however, that the fibers in such fiber‐reinforced composites may show significant curvature, in particular for long fibers. The work at hand introduces an extension of the original SAM approach to curved fibers. More precisely, curved fibers are considered as sequences of straight fibers which are joined at their respective ends and whose level of bending is controlled by the angle between adjacent fiber segments. We discuss how to efficiently implement the novel method and how to select the crucial numerical parameters. We compare the introduced methodology to the original SAM algorithm for short fibers and demonstrate the superiority of the novel strategy for long fibers.