Abstarct: In present study unsteady flows are viscoelastic fluids are studied. The focus of study is on flows in closed channel. In first step numerical algorithms are compared. Fractional step was used to solve simple Coette flow. This method is suitable for shear flows like Coette flow and flow between two circulating cylinders. But this method doesn’t work for pressure driven flows. This algorithm has problems with problems that include flows. PISO and SIMPLEST are best algorithms for unsteady viscoelastic flows in FVM method. OpenFOAM is open-source software that include have codes which solve viscoelastic fluid flows with PISO algorithm. This software was used to solve flows equations. In order to solve n simple flows, an applied flow was selected. This flow is blood flow in arteriole. In former study has shown than blood has viscoelastic properties in small vessels. For this purpose a non-linear viscoelastic model was used. There isn’t any study which simulates blood with non-linear viscoelastic models. Giesekus model was used in this study. It’s shown that only non-linear viscoelastic models can describe blood viscosity behavior in small shear rates. Best magnitude for Giesekus models constant was derived by using experimental data about changing blood viscosity with shear rate. Experimental data about velocity in arteriole of mouse was used for inlet velocity. Results shown that Giesekus model have good ability to simulate wall shear stress of blood. Secondary flow in straight pipes with non-circular cross section is a classical problem in non-Newtonian fluid mechanics. There are many studies about this flow. But there isn’t any study about unsteady case of this problem. Present work is first study about unsteady flows of secondary flows in straight pipes. Flow was simulated in straight pipe with square cross section. Flow was solved in three dimensions. Fully developed condition was used for inlet and outlet. This assumption reduced grid size but equations are solved in three dimensions. Effects of elastic number and mobility factor were studied. Flow is pressure driven. There are oscillations in starting of flows. Amplitude of oscillations has increased by increasing elastic number and mobility factor. Frequency of oscillations was decreased by increasing elastic number and mobility factor.