The blood flow through the Bidirectional Glenn shunt (BGS) and modified Blalock-Taussig shunt (mBTS) to the pulmonary arteries (PAs) was analyzed using Computational Fluid Dynamics. This study consisted of the steady and pulsatile cases. In case one, the results of blood flow through the BGS for the Newtonian and non-Newtonian viscosity models were compared. Case two focused on having an additional pulsatile blood flow through the mBTS using the non-Newtonian Carreau viscosity model. The geometries were created based on the angiograms. In case one, boundary conditions to be specified at the inlets were obtained from the flow rate measurements via Doppler flow studies in children and young adults. The averaged velocities were obtained from these flow rates and specified as parabolic velocity profiles at the inlets. The average PA pressures were obtained from the catheterization data and specified at the branches of the PA outlets. In case two, boundary conditions at the same inlets were constant during the cardiac cycle. The pulsatile PA and aortic pressure tracings obtained from the catheterization data were specified at the outlets and mBTS inlet, respectively. A comparison is made between the first and second case results.