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Currently the best prospect for detecting Weakly Interacting MassiveParticles (WIMPs) is via the annual modulation, which occurs due to the Earth'srotation around the Sun, of the direct detection signal. We investigate theeffect of uncertainties in our knowledge of the structure of the galactic haloon the WIMP annual modulation signal. We compare the signal for threenon-standard halo models: Evans' power-law halos, Michie models with anasymmetric velocity distribution and Maxwellian halos with bulk rotation. Wethen compare the theoretical predictions of these models with the experimentalsignal found by the DAMA experiment and investigate how the WIMP mass andinteraction cross section determined depend on the halo model assumed. We findthat the WIMP mass confidence limits are significantly extended to largermasses, with the shape of the allowed region in the mass-cross section planedepending on the model.Comment: 6 pages, 6 .ps figures, final version to appear in Phys. Rev. D,  figs. 1-3 replotted for clarity, minor changes to discussio

Weakly interacting massive particle annual modulation signal and nonstandard halo models