<p>The unsteady flow of a Newtonian fluid through an inclined porous channel is investigated. The permeability ratio and anisotropic angle characterize the anisotropic permeability of a porous medium. The flow is governed by the Brinkman model and and driven by a constant pressure gradient. The appropriate initial and no-slip boundary conditions are assumed. The non-linear partial differential equation is solved by the Crank–Nicolson finite-difference approach to obtain the numerical results of velocity profiles for different physical parameters. The findings indicate that fluid achieves its maximum velocity when the permeability ratio is less than 1 and its minimum for greater than 1. Additionally, an increase in the deviation of the anisotropic angle and channel’s inclination decreases fluid velocity. The impact of gravity increases with the channel’s inclination.</p>