Background: 3D bioprinting is the future of constructing functional organs. Creating a bioactive scaffold with pancreatic islets presents many challenges. The aim of this paper is to assess how the 3D bioprinting process affects islet viability. Methods: The BioX 3D printer (Cellink), 600 μm inner diameter nozzles, and 3% (w/v) alginate cell carrier solution were used with rat, porcine, and human pancreatic islets. Islets were divided into a control group (culture medium) and 6 experimental groups (each subjected to specific pressure between 15 and 100 kPa). FDA/PI staining was performed to assess the viability of islets. Analogous studies were carried out on α-cells, β-cells, fibroblasts, and endothelial cells. Results: Viability of human pancreatic islets was as follows: 92% for alginate-based control and 94%, 90%, 74%, 48%, 61%, and 59% for 15, 25, 30, 50, 75, and 100 kPa, respectively. Statistically significant differences were observed between control and 50, 75, and 100 kPa, respectively. Similar observations were made for porcine and rat islets. Conclusions: Optimal pressure during 3D bioprinting with pancreatic islets by the extrusion method should be lower than 30 kPa while using 3% (w/v) alginate as a carrier.