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Cardiovascular disease is now under the influence of several factors that encourage researchers to investigate the flow of these vessels. Oscillation influences the blood circulation in the volume of red blood cells (RBC) strongly. Therefore, in this study, its effects have been considered on hemodynamic parameters in the elastic wall and coronary bifurcation. In this study, a 3D geometry of non-Newtonian and pulsatile blood circulation is considered in the left coronary artery bifurcation. The Casson model with various hematocrits is analyzed in elastic and rigid walls. The wall shear stress (WSS) cannot show the stenosis artery alone, therefore, the oscillatory shear index (OSI) is represented as a hemodynamic parameter of WSS individually of time. The results are determined using two-way fluid-structure interaction (FSI) coupling method using an arbitrary Lagrangian-Eulerian method. The most prominent difference in velocity happened in the bifurcation and at hematocrit 30 with yield stress 6.59E-04 Pa. The backflow and vortex flow in the LCx branch grown with increasing shear rates. The likelihood of plaque generation at the ending of the LM branch is observed in hematocrits 10 and 20, while the WSS magnitude is normal in the hematocrit 60 with the greatest yield stress in the bifurcation. The shear stress among the rigid and elastic models is the highest at the ending of the LM branch. The wall shear stress magnitude among the models decreased at most of 24.49% by dividing the flow. Time-independent results for models showed that there is the highest value of OSI at the bifurcation, which then quickly dropped.