  We study the cohesive energy and elastic properties as well as normal modes
of the Wigner and bubble crystals of the two-dimensional electron system (2DES)
in higher Landau levels. Using a simple Hartree-Fock approach, we show that the
shear moduli ($c_{66}$'s) of these electronic crystals show a non-monotonic
behavior as a function of the partial filling factor $\nu^*$ at any given
Landau level, with $c_{66}$ increasing for small values of $\nu^*$, before
reaching a maximum at some intermediate filling factor $\nu^*_m$, and
monotonically decreasing for $\nu^*>\nu^*_m$. We also go beyond previous
treatments, and study how the phase diagram and elastic properties of electron
solids are changed by the effects of screening by electrons in lower Landau
levels, and by a finite thickness of the experimental sample. The implications
of these results on microwave resonance experiments are briefly discussed.
