We report on studies of spin structures that appear around screw and edge dislocations in Dy (0001) films grown on W (110) substrates. By means of spin-polarized scanning-tunneling microscopy, we have observed the formation of vortexlike and lobe-shaped magnetic structures. We have studied the effect of fundamental dislocations in micromagnetic simulations by including the magnetoelastic interactions in addition to the usually considered energy terms which arise from the magnetocrystalline anisotropy and the exchange energies. Starting from actual physical parameter values for Dy, our calculations are in qualitative and quantitative agreement with the size and the shape of the spin structures experimentally observed.