Tissue regeneration with scaffolds has proven promising for the repair of damaged tissues or organs. Dispensing-based printing techniques for scaffold fabrication have drawn considerable attention due to their ability to create complex structures layer-by-layer. When employing such printing techniques, the flow rate of the biomaterial dispensed from the needle tip is critical for creating the intended scaffold structure. The flow rate can be affected by a number of variables including the material flow behavior, temperature, needle geometry, and dispensing pressure. As such, model equations can play a vital role in the prediction and control of the flow rate of the material dispensed, thus facilitating optimal scaffold fabrication. This paper presents the development of a model to represent the flow rate of medium viscosity alginate dispensed for the purpose of scaffold fabrication, by taking into account the shear and slip flow from a tapered needle. Because the fluid flow behavior affects the flow rate, model equations were also developed from regression of experimental data to represent the flow behavior of alginate. The predictions from both the flow behavior equation and flow rate model show close agreement with experimental results. For varying needle diameters and temperatures, the slip effect occurring at the needle wall has a significant effect on the flow rate of alginate during scaffold fabrication.