Abstarct: In lots of applications such as oil recovery and chemistry laboratories in order to separate different phases of liquids, Soffman-Taylor instability appears. This instability starts with injection of less viscous fluid into higher viscous fluid and some patterns similar to fingers of a hand start to form. At current research, the effect of elasticity of displacing fluid on an immiscible displacement has been investigated in a porouse media denced with glass beads, experimentally. In all experiments, silicon oil is used as displaced fluid and a mixture of glycerin, water and polyacrilamid powder known as displacing fluid. Different viscoelastic fluids by different mass percen ranging from 50ppm to 400ppm have been produced by means of high accuracy equipment in labrotary. Viscoelastic fluids until 100ppm are known as Boger wich has constant viscousity versus shear rate. Higher denced polymer fluids are shear-thining wich has different viscousity by each shear rate. Experiments showed, in Newtonian displacement very small and tiny fingers similar to arterioles of human body formed. This tiny fingers further disperse all over the set-up and the bulk of the displacing fluid, follow the tiny fingers. By injecting highr denced polymer fluids, the number of tiny fingers reduces and a uniform front with less number of fingers and thicker fingers will form. Increasing density of polymer leads to more viscoelastic properties such as normal stress and elastic viscousity which conclude to a better displacement. The best desirable result was noted for 400ppm fluid. Mixing length and Sweep efficiency are two parameters to report the results. By increasing Blake number and viscousity ratio mixing length increases and sweep efficiency decreases. Also by increase of polymer in the solution, there will be a better sweep efficiency.