Tissue vascularization is critical to enable oxygen and nutrient supply. Therefore, establishing expedient vasculature is necessary for the survival of tissue after transplantation. The use of biomechanical forces, such as cell-induced traction forces, may be a promising method to encourage growth of the vascular network. Three-dimensional (3D) bioprinting, which offers unprecedented versatility through precise control over spatial distribution and structure of tissue constructs, can be used to generate capillary-like structures in vitro that would mimic microvessels. This study aimed to develop an in vitro, 3D bioprinted tissue model to study the effect of cellular forces on the spatial organization of vascular structures and tissue maturation. The developed in vitro model consists of a 3D bioprinted polycaprolactone (PCL) frame with a gelatin spacer hydrogel layer and a gelatin-fibrin-hyaluronic acid hydrogel layer containing normal human dermal fibroblasts and human umbilical vein endothelial cells printed as vessel lines on top. The formation of vessel-like networks and vessel lumens in the 3D bioprinted in vitro model was assessed at different fibrinogen concentrations with and without inhibitors of cell-mediated traction forces. Constructs containing 5 mg/ml fibrinogen had longer vessels compared to the other concentrations of fibrinogen used. Also, for all concentrations of fibrinogen used, most of the vessel-like structures grew parallel to the direction the PCL frame-mediated tensile forces, with very few branching structures observed. Treatment of the 3D bioprinted constructs with traction inhibitors resulted in a significant reduction in length of vessel-like networks. The 3D bioprinted constructs also had better lumen formation, increased collagen deposition, more elaborate actin networks, and well-aligned matrix fibers due to the increased cell-mediated traction forces present compared to the non-anchored, floating control constructs. This study showed that cell traction forces from the actomyosin complex are critical for vascular network assembly in 3D bioprinted tissue. Strategies involving the use of cell-mediated traction forces may be promising for the development of bioprinting approaches for fabrication of vascularized tissue constructs.