A numerical model is developed to analyse the interaction of artificial cilia with the surrounding fluid in a three-dimensional setting in the limit of vanishing fluid inertia forces. The cilia are modelled using finite shell elements and the fluid is modelled using a boundary element approach. The coupling between both models is performed by imposing no-slip boundary conditions on the surface of the cilia. The performance of the model is verified using various reference problems available in the literature. The model is used to simulate the fluid flow due to magnetically actuated artificial cilia. The results show that narrow and closely spaced cilia create the largest flow, that metachronal waves along the width of the cilia create a significant flow in the direction of the cilia width and that the recovery stroke in the case of the out-of-plane actuation of the cilia strongly depends on the cilia width. © 2012 Cambridge University Press.