  We show that models of strongly interacting (SIMP) dark matter built to
reproduce the DAMA signal actually cannot account for its time dependence. We
discuss the constraints on this type of models coming from direct detection
experiments and study the propagation of thermalised dark matter particles in
the ground for the allowed values of the parameters. We consider a simple 1D
diffusion and a more detailed 3D diffusion. In both cases the predicted signal
has either the wrong phase of the annual modulation or a much larger amplitude
of the diurnal modulation.
