  We studied the high-order harmonic generation (HHG) from 2D solid materials
in circularly and bichromatic circularly polarized laser fields numerically by
simulating the dynamics of single-active-electron processes in 2D periodic
potentials. Contrary to the absence of HHG in the atomic case, circular HHGs
below the bandgap with different helicities are produced from intraband
transitions in solids with $C_4$ symmetry driven by circularly polarized
lasers. Harmonics above the bandgap are elliptically polarized due to the
interband transitions. High-order elliptically polarized harmonics can be
generated efficiently by both co-rotating and counter-rotating bicircular
mid-infrared lasers. The cutoff energy, ellipticity, phase, and intensity of
the harmonics can be tuned by the control of the relative phase difference
between the 1$\omega$ and 2$\omega$ fields in bicircularly polarized lasers,
which can be utilized to image the structure of solids.
