  Ultraflat bands in twisted bilayers of two-dimensional materials have
potential to host strong correlations, including the Mott-insulating phase at
half-filling of the band. Using first principles density functional theory
calculations, we show the emergence of ultraflat bands at the valence band edge
in twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. The
computed band widths, 5 meV and 23 meV for 56.5$^\circ$ and 3.5$^\circ$ twist
angles respectively, are comparable to that of twisted bilayer graphene near
'magic' angles. Large structural transformations in the Moir\'e patterns lead
to formation of shear solitons at stacking boundaries and strongly influence
the electronic structure. We extend our analysis for twisted bilayer MoS$_2$ to
show that flat bands can occur at the valence band edge of twisted bilayer
WS$_2$, MoSe$_2$ and WSe$_2$ as well.
