Simulations of blood flow as a porous medium through an elbow artery have been investigated. The arteries have treated as a porous medium. The blood is represented as a Newtonian fluid. The blood is supplied with various geometries of arteries, which have different diameters. The no-slip boundary condition is applied for velocity components along the rigid arterial walls. Numerical simulations have presented the details of blood flow patterns and the local distribution of blood flow along the artery. The effects of permeability, with respect to the changes in the Reynolds number (Re = 0.1,1 and 5) as well for varying porosity levels has been discussed. The effect of blood vessel diameter on the resultant of distribution of velocity inside the vessel has been studied. Results are presented in the form of variations of velocity distributions and local variations of flow rates through the vessel dimensions. The numerical results of simulation are compared with the available data and a good agreement is found. The study shows to be potentially useful to evaluate the role of porosity and flow conditions when the body is subjected to diseases.