Polymer solutions are often described as viscoelastic fluids, whose rheological behavior dynamically evolves according to the flow shear rate due to successive contractions and relaxations of inner deformable components. Contrary to shear-thickening and shear-thinning fluids, viscoelastic fluids can undergo an increase in the normal stress-differences even in simple geometries, leading to counterintuitive flow patterns. In this paper, we investigate numerically the monophasic flow of viscoelastic fluids through microfluidic devices. The objective is to qualitatively assess how modification of the rheological properties and the geometry of porous media representative element affect the flow regime at microscale. Deviations from equivalent Newtonian model are analyzed to quantify the contribution of elasticity in the flow. It is demonstrated that depending on the geometry, flow of polymer solution can display anisotropic features and flow resistance at relatively low viscoelastic numbers, which is coherent with previous microscopic experimental and numerical studies. Ensued applications of the formulated microscale model are discussed.