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Adhering cells exert traction forces on the underlying substrate. We numerically investigate the intimate relation between traction forces, the structure of the actin cytoskeleton, and the shape of cells adhering to adhesive micropatterned substrates. By combining the Cellular Potts Model with a model of cytoskeletal contractility, we reproduce prominent anisotropic features in previously published experimental data on fibroblasts, endothelial cells, and epithelial cells on adhesive micropatterned substrates. Our work highlights the role of cytoskeletal anisotropy in the generation of cellular traction forces, and provides a computational strategy for investigating stress fiber anisotropy in dynamical and multicellular settings.Author summaryCells that make up multicellular life perform a variety of mechanical tasks such as pulling on surrounding tissue to close a wound. The mechanisms by which cells perform these tasks are, however, incompletely understood. In order to better understand how they generate forces on their environment, cells are often studied in vitro on compliant substrates, which deform under the so called “traction forces” exerted by the cells. Mathematical models complement these experimental approaches because they help to interpret the experimental data, but most models for traction forces on adhesive substrates assume that cells contract isotropically, i.e., they do not contract in a specific direction. However, many cell types contain organized structures of stress fibers - strong contracting cables inside the cell - that enable cells to exert forces on their environment in specific directions only. Here we present a computational model that predicts both the orientations of these stress fibers as well as the forces that cells exert on the substrates. Our model reproduces both the orientations and magnitudes of previously reported experimental traction forces, and could serve as a starting point for exploring mechanical interactions in multicellular settings.