Typically, tissue-engineered scaffolds mimic the topographical properties of the native extracellular matrix. However, other physical properties, such as the scaffold mechanical stiffness, are not imitated. The purpose of this study was to fabricate scaffolds with improved mechanical properties and investigate their biocompatibility towards endothelial cells and platelets. To enhance mechanical properties, an electrospinning apparatus was developed that fabricates fibers with sheath-core morphologies. Different combinations of cellulose acetate and chitosan were chosen to modulate the mechanical properties of the formed fibers. We hypothesized that mechanically stiffer scaffolds would improve endothelial cell growth and that all scaffolds would be compatible towards endothelial cells and platelets. Endothelial cell-culture conditions were quantified up to 5 days. Migration onto scaffolds was monitored for 10 days. Platelet aggregation, antagonized by thrombin receptor agonist peptide 6, was measured after scaffold incubation. A platelet activation time-course was assessed with the modified prothrombinase assay. As scaffold mechanical stiffness increased, endothelial cell growth within and adhesion to and migration throughout the scaffolds was promoted. Also, scaffolds did not induce platelet aggregation or activation. These results indicate that the mechanical stiffness of engineered scaffolds regulates endothelial cell-culture parameters and that these sheath-core electrospun scaffolds are compatible towards endothelial cells and platelets.