In this paper, we present two-dimensional modeling and simulation of blood vessel using COMSOL Multiphysics. The rationale behind this study is that mathematical modeling and numerical simulation can lead to better understanding of the phenomena involved in vascular diseases. This study assumes that the fluid is laminar, non-Newtonian, viscous and compressible and the arterial wall is elastic. Parameters of blood vessel were assigned to the wall and parameters for fat deposits to the blockages. Blood is an example of a non-Newtonian fluid applied to the model in the present simulations. Structural deformation and fluid dynamics are determined simultaneously.