Summary: The paper presents a linear stability analysis of a one-dimensional stationary flow through a poroelastic medium. This base flow is perturbed in four ways: by longitudinal one-dimensional disturbances without and with mass exchange, and by transversal two-dimensional disturbances without and with mass exchange. The eigenvalue problem for the first step field equations is solved using a finite difference scheme. For both disturbances without mass exchange results are confirmed by an analytical solution. We present the stability and relaxation properties in dependence on the two most important model parameters, namely the bulk and surface permeability coefficients.