This work is concerned with deriving a macroscopic ®ltration law for describing transient linear viscoelastic ¯uid ¯ow in porous media. This is performed using a homogenisation technique, i.e. by upscaling the heterogeneity scale description. The macroscopic ®ltration law is expressed in Fourier space as a generalised Darcy's law with a dynamic permeability tensor. This model is valid at low Reynolds and Deborah numbers. Analytical results are determined in the particular case of the ¯ow of an Oldroyd ¯uid in a bundle of capillary tubes and are compared to those obtained by a corresponding phenomenological model.
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