  We investigate single and two-component scalar dark matter scenarios in
classically scale invariant standard model which is free of the hierarchy
problem in the Higgs sector. We show that despite the very restricted space of
parameters imposed by the scale invariance symmetry, both single and
two-component scalar dark matter models overcome the direct and indirect
constraints provided by the Planck/WMAP observational data and the LUX/Xenon100
experiment. We comment also on the radiative mass corrections of the
classically massless scalon that plays a crucial role in our study.
