Three-dimensional (3D) bioprinting offers transformative potential for cardiac tissue engineering by enabling the fabrication of cell-laden constructs. Yet, key challenges persist, including maintaining cell viability within bioprinted constructs and clarifying how embedded cells influence their physical and mechanical properties. This study addresses these challenges by incorporating human umbilical vein endothelial cells (HUVECs) into alginate-gelatin hydrogels for bioprinting constructs and then evaluating the impact of the incorporated cells on mechanical, physical, and rheological properties. Bioinks or hydrogels were prepared with or without HUVECs, and their rheological properties were assessed. Computational fluid dynamics (CFD) simulation was employed to identify the suitable bioprinting pressure for bioprinting, while minimizing cell damage. Constructs were designed and 3D printed with a structure of an angular pattern to replicate the orientation of heart myofibrils and then characterized over a 21-day period for viscoelasticity, elastic modulus, swelling, mass loss, morphology, and cell viability.The incorporation of cells increased storage and loss moduli of the bioink, demonstrating shear-thinning behavior as modeled by the Cross model. CFD simulation and preliminary cell viability assays identified 25 kPa as the most appropriate 3D printing pressure among those examined, effectively maintaining cell viability post-bioprinting. Both cell-free and cell-laden constructs exhibited viscoelastic properties; however, cell-laden constructs had a lower elastic modulus under linear compression, reduced swelling percentage, and greater mass retention. Notably, high cell viability was observed immediately post-bioprinting and was sustained for over one week. The incorporation of endothelial cells into alginate-gelatin hydrogel significantly modulates the rheological properties of the bioink, thereby influencing the mechanical / physical properties and cell viability of the bioprinted constructs. These findings provide a foundational framework for developing structurally robust and cell-laden constructs with enhanced functional fidelity, supporting their potential application in cardiac tissue engineering.