The detailed distribution of mass within clusters of galaxies can be used to probe the nature of dark matter. We show that constraints on the extent of the mass distribution around galaxies in the rich cluster A2218 obtained from combining strong and weak lensing observations are consistent with the predictions which assume that the dominant mass component (dark matter) in these halos is collisionless. A strongly interacting (fluid-like) dark matter is ruled-out at a confidence level of more than 5sigma.