A common method of drying cereal grains is to ventilate a large static mass of grain with an even how of air at near ambient temperature. After the grain has been dried it is often stored in the same container and kept cool by aeration with a lower velocity of air than is used in drying. To analyse the airflow through this mass of grain a nonlinear momentum equation for flow through porous media is used where the resistance to flow is a + b\upsilon\. This equation, together with the assumption that the air is incompressible, defines the problem which is solved numerically, using the finite element method, and the results compared with experimental values. The small parameter epsilon = b upsilon(tau)/a, where upsilon(tau) is the velocity scale, is used in a perturbation analysis to-examine the nonlinear effects of the resistance on the airflow. When epsilon = 0 the equations reduce to those for potential flow, while for small values of epsilon there are first-order corrections to the pressure p(1) and the stream function chi(1). The nonlinear problem is simplified by changing to curvilinear coordinates (s, t) where s is constant on the potential flow isobars while t is constant on the streamlines. General conclusions are derived for p(1) and chi(1), for example that they depend on the curvature of the potential flow solution with a large curvature of the isobars leading to larger values of pr and similarly for the streamlines. The potential flow solution p(0) and the first order solution p(0) + epsilon p(1) are close to the solution of the full nonlinear problem when epsilon is small. To illustrate this for a typical grain storage problem, the solution po is shown to be very close to the finite element solution (with a difference of less than 1%) when epsilon < 0.03 while for the first order solution p(0) + epsilon p(1) the difference is less than 1% when epsilon < 0.1.