Abstarct: This study presents a numerical investigation in order to understand the flow characteristics of a viscoelastic fluid in the porous media through a hyperbolic wavy hele-shaw cell. The simulated geometry is a two-dimensional rectangular hele-shaw cell with hyperbolic wavy walls subjected to a constant extension rate. The PTT (Phan-Thien and Tanner) constitutive model is employed to predict the rheological behavior of the viscoelastic fluid. The governing equations, including continuity, momentum, and the PTT constitutive equation, are solved numerically using the finite-volume method implemented within the open-source software OpenFOAM. The main aim of this study is using a special shape of waves that brings a moderate constant elongational viscosity in the whole of cell. The influence of various dimensionless parameters, such as the elasticity number, viscosity ratio, epsilon number, slip parameter, contraction ratio, Weissenberg number, and dimensionless wave length, on the viscoelastic fluid flow is systematically investigated. Results are presented in terms of dimensionless quantities, with a focus on the velocity, von-mises stress, wall shear stress components, pressure drop, streamlines, principal stress difference, and flow patterns. The results indicate that, within the considered parameter range, the viscoelastic fluid flows through the cavity without exhibiting any vortices, instabilities, or different flow patterns. This observation provides valuable insights in the behavior of viscoelastic fluids within the porous media. Various instabilities may arise in this system, such as elastic instability (which occurs due to the elastic properties of the fluid and its interaction with the geometry of the cell) and fingering instability (which arises at the interface of two fluids with differing viscosities). Studying instabilities in this system is crucial for a better understanding of mass and energy transfer mechanisms, as well as for the design of more efficient microfluidic systems. A detailed discussion of the aforementioned dimensionless parameters and their impact on the flow characteristics is provided.