A fluid mechanical model is developed for the filtering mechanism in mussels that enables estimates to be made of the pressure drop through the gill filaments due to (i) the latero-frontal filtering cilia, (ii) the lateral (pumping) cilia and through the non-ciliated zone at the ventral end of the filament. Calculations indicate that the lateral cilia can generate a sufficient pressure change to 'pump' water through the gill filaments. The velocity profile across the filaments indicates that a backflow can occur in the centre of the channel. Normally the latero-frontal cilia would damp out this backflow but in the case when all the cilia are upright, two 'standing' eddies may form at the mouth of the channel, forcing the incoming water to the side.