3D bioprinting with cell containing bioinks show great promise in the biofabrication of patient specific tissue constructs. To fulfil the multiple requirements of a bioink, a wide range of materials and bioink composition are being developed and evaluated with regard to cell viability, mechanical performance and printability. It is essential that the printability and printing fidelity is not neglected since failure in printing the targeted architecture may be catastrophic for the survival of the cells and consequently the function of the printed tissue. However, experimental evaluation of bioinks printability is time-consuming and must be kept at a minimum, especially when 3D bioprinting with cells that are valuable and costly. This paper demonstrates how experimental evaluation could be complemented with computer based simulations to evaluate newly developed bioinks. Here, a computational fluid dynamics simulation tool was used to study the influence of different printing parameters and evaluate the predictability of the printing process. Based on data from oscillation frequency measurements of the evaluated bioinks, a full stress rheology model was used, where the viscoelastic behaviour of the material was captured. Simulation of the 3D bioprinting process is a powerful tool and will help in reducing the time and cost in the development and evaluation of bioinks. Moreover, it gives the opportunity to isolate parameters such as printing speed, nozzle height, flow rate and printing path to study their influence on the printing fidelity and the viscoelastic stresses within the bioink. The ability to study these features more extensively by simulating the printing process will result in a better understanding of what influences the viability of cells in 3D bioprinted tissue constructs.