A macroscopic model for non-steady and inertial one-phase incompressible flow in rigid porous media is presented using an upscaling technique. The resulting model is non-local in time and involves two effective coefficients, namely, a dynamic apparent permeability tensor and a vector accounting for the time-decaying influence of the flow initial condition. Ancillary closure problems are provided, which allow computing the effective coefficients. Symmetry and positiveness analyses of the apparent permeability are carried out. The performance of the macroscopic model for different macroscopic forcing is examined along with validation with direct numerical simulations. It is shown that the purely heuristic classical model, consisting in a Darcy-like model complemented with an accumulation term on the filtration velocity, is not appropriate.