Viscoelastic flow in channel having transient hydrodynamic behavior, filled with and without porous medium is addressed. The boundary value problem is investigated through analytical and numerical solutions, for the governing system of partial differential equations, arising in the study for flow of viscoelastic fluids. Analytical solutions in terms of velocity, normal stress and shear stress at different values of time, viscosity and Darcy\'s number are obtained for constant viscosity Oldroyd-B constitutive model. Lie group technique is adopted to find solutions through symmetry of differential equations, whilst numerical solutions are realized by employing ND Solve, Mathematica Solver. Lie group technique is compared against numerical solutions by employing ND Solve, Mathematica Solver. The analytical solutions are observed in good agreement with the numerical solutions.