Fibronectins (FNs) are a major component of the extracellular matrix (ECM), and provide important binding sites for a variety of ligands outside and on the surface of the cell. Similar to other ECM proteins, FNs are consistently subject to mechanical stress in the ECM. Therefore, it is important to study their structure and binding properties under mechanical stress and understand how their binding and mechanical properties might affect each other. Although certain FN modules have been extensively investigated, no simulation studies have been reported for the FN type I (Fn1) domains, despite their prominent role in binding of various protein modules to FN polymers in the ECM. Using equilibrium and steered molecular dynamics simulations, we have studied mechanical properties of Fn1 modules in the presence or the absence of a specific FN-binding peptide (FnBP). We have also investigated how the binding of the FnBP peptide to Fn1 might be affected by tensile force. Despite the presence of disulfide bonds within individual Fn1 modules that are presumed to prevent their extension, it is found that significant internal structural changes within individual modules are induced by the forces applied in our simulations. These internal structural changes result in significant variations in the accessibility of different residues of the Fn1 modules, which affect their exposure, and, thus, the binding properties of the Fn1 modules. Binding of the FnBP appears to reduce the flexibility of the linker region connecting individual Fn1 modules (exhibited in the form of reduced fluctuation and motion of the linker region), both with regard to bending and stretching motions, and hence stabilizes the inter-domain configuration under force. Under large tensile forces, the FnBP peptide unbinds from Fn1. The results suggest that Fn1 modules in FN polymers do contribute to the overall extension caused by force-induced stretching of the polymer in the ECM, and that binding properties of Fn1 modules can be affected by mechanically induced internal protein conformational changes in spite of the presence of disulfide bonds which were presumed to completely abolish the capacity of Fn1 modules to undergo extension in response to external forces.