The blood flow under physiologic conditions is an important field of study. Detection and quantification of the normal and abnormal blood flow in vessels serve as basis for diagnosis and/or surgical planning. The blood flow complex characteristics have been investigated through simulations based on mathematical models that include constitutive equations describing the hemodymanics and its relations with the deformable vessels wall. The computational techniques applied to model the blood flow in the circulatory system investigated either the velocity field or the pressure field, but not both of them in the same time, treating the vessel walls as rigid ones or considering significantly simplified or reduced geometries for the deformable wall models. The approximation of rigid-walls was made mostly due to the difficulty of solving the coupled blood flow/vessel deformation problem and was justified by the observation that, under normal conditions, wall deformability does not significantly alter the velocity field. Modeling of the three-dimensional blood flow in compliant vessels is extremely challenging for a number of additional reasons such as: geometry acquisition, accurate constitutive description of the behavior and induced movement of the tissue, inflow and outflow boundary conditions, etc. The computational fluid dynamics (CFD) technique is applyed to describe the blood flow in a segment of portal vein system. The reconstructed model of the vessels provides geometric boundaries for the CFD blood flow model. In this respect a finite difference grid is going to be generated over the finite element model geometry. Hemodymanics parameters such as velocity magnitude, pressure and wall shear stress are going to be computed.