A multi-domain finite element formulation has been applied to determine the semi-solid permeability of an equiaxed granular structure. The granular model was constructed from a Voronoï tessellation algorithm. The liquid-solid interface is represented implicitly by a level set function, and an anisotropic meshing technique is employed for an accurate description of the interface geometry with reasonable computation resources. The liquid phase is considered as an incompressible Newtonian fluid, and permeability is computed based on Darcy's law. A good agreement is found with available literature data and with the Kozeny-Carman prediction. The proposed method, associating the finite element method with a level set framework, is shown to be an effective technique for examining microstructure effects on the semi-solid permeability. This is illustrated by considering the influence of the Gibbs-Thomson effect. © 2010 Elsevier B.V. All rights reserved.