  The annual modulation in the rate of WIMP recoils observed by the DAMA
collaboration at high significance is often analyzed in the context of an
isothermal Maxwell-Boltzmann velocity distribution. While this is the simplest
model, there is a need to consider other well motivated theories of halo
formation. In this paper, we study a different halo model, that of self similar
infall which is characterized by the presence of a number of cold streams and
caustics, not seen in simulations. It is shown that the self similar infall
model is consistent with the DAMA result both in amplitude and in phase, for
WIMP masses exceeding $\approx$ 250 GeV at the 99.7% confidence level. Adding a
small thermal component makes the parameter space near $m_\chi$ = 12 GeV
consistent with the self similar model. The minimum $\chi^2$ per degree of
freedom is found to be 0.92(1.03) with(without) channeling taken into account,
indicating an acceptable fit. For WIMP masses much greater than the mass of the
target nucleus, the recoil rate depends only on the ratio $\sigma_{\rm
p}/m_\chi$ which is found to be $\approx$ 0.06 femtobarn/TeV. However as in the
case of the isothermal halo, the allowed parameter space is inconsistent with
the null result obtained by the CDMS and Xenon experiments for spin-independent
elastic scattering. Future experiments with directional sensitivity and mass
bounds from accelerator experiments will help to distinguish between different
halo models and/or constrain the contribution from cold flows.
