Abstarct: During past decades analysis over fluid flow in curved conduits been considered as one of the benchmark problem in fluid flow investigations stemming from its wide range of applications in related industry and medicine investigations. This topic has been studied via lots of experimental, numerical and analytical methods. It should be Noted that most of investigation, so far, are limited to cases with Newtonian fluids, with few considering non-Newtonian fluids. In the current research, both the viscoelastic flow and heat transfer in stationary dean conduit with rectangular cross section has been investigated. To analyze the effect of viscoelasticity in this geometry the famous non-linear Giesekus constitutive equation is implemented. In the presented work, the regular finite difference method has been used to discrete governing equations using the staggered mesh technics and allocating method of flow and heat transfer parameters on this mesh is according to the Marker and Cell method. Artificial To estimate the pressure in time steps of numerical simulation the compressibility method is applied . The accuracy of the presented numerical results is checked for different bench mark cases and independency of the results from mesh size is also accurately investigated. In following the mutual effects of parameters such as Reynolds number, Dean Number, Prandtel number, curvature ratio, alpha and beta parameters of the constitutive equation, Weissenberg Number, aspect ratio and effect of viscosity on the flow field and heat transfer has been widely studied. It is shown that as the viscoelasticity effects are amplified, the flow resistance in decreased that can be attributed to the pattern of flow distribution . In heat transfer investigation, the effect of these parameters on flow distribution is investigated. It is illustrated that in the isothermal scenario the temperature distribution cannot get into its fully developed distribution.