An annual modulation in the event rate of the NaI detector of the DAMA collaboration has been used to infer the existence of particle dark matter in the Galactic halo. Bounds on the WIMP mass and WIMP-nucleon cross section have been derived. These analyses have assumed that the local dark-matter velocity distribution is either isotropic or has some bulk rotation. Here we consider the effects of possible structure in the WIMP velocity distribution on the annual-modulation amplitude. We show that if we allow for a locally anisotropic velocity dispersion tensor, the interpretation of direct detection experiments could be altered significantly. We also show that uncertainties in the velocity distribution function that arise from uncertainties in the radial density profile are less important if the velocity dispersion is assumed to be isotropic.
