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We perform a non-modal stability analysis of a fully-developed and laminar flow of an incompressible fluid through a channel bounded by flat, homogeneous, isotropic porous layers. We model the flow in the purely fluid region using the Navier-Stokes equations, and the flow through the porous layers using a volume- averaged version of the Navier-Stokes equations (VANS) derived by Whitaker (1994). We restrict our study to flows through porous materials in which inertial effects can be considered negligible. We assume an exponential temporal dependence of the perturbations and derive the modal equations. We discretize the modal equations by means of the Chebyshev collocation spectral method, solve the related linear stability problem, and compute the maximum energy amplification among all the possible perturbations. We use an adaptive algorithm to carry out a parametric study in which we vary Reynolds number, streamwise and spanwise wavenumbers, permeability, porosity and a coefficient which represents the momentum transfer process at the interface between the fluid region and the porous material. We validate our methodology by comparing our eigenvalues with the ones reported by previous linear stability studies, as well as by recovering the transient energy growth of the plane Poiseuille flow, in the limit of zero permeability. We report that in well defined regions of the wavespace, permeability can increase the maximum value of the energy growth up to 40% with respect of plane Poiseuille flow. We show that this increase is associated to an optimal initial condition in which there is a significant flow across the interface. Moreover, we discover that the modes associated with the equations governing the fluid motion in the porous layers and with the momentum transfer conditions, do not contribute significantly to reported amplification of the maximum value of the energy growth function. We find that porosity and momentum transfer coefficient have a weaker influence on the transient growth than permeability does, while they alter significantly the linearly unstable regions in the wavespace.