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Numerical simulation of flow through stenotic artery is performed using spectral element method in an axisymmetric geometry. This method, under suitable conditions, provides high accuracy. The use of the weak form of the governing model equations, brings flexibility in treating solution domains with nonstandard geometry. The solenoidal character of the flow is preserved by the treatment of the pressure in a natural way in the numerical formulation. The use of Legendre-Lobatto grid points with its denser distribution near the boundaries increases the ability of the grid to resolve the flow boundary layer. This study is aimed as the first step in the development of the technique.