  We present a first-principles study of effects of small biaxial strain
($|\varepsilon|\le 5\%$) and perpendicular electric field (E-field) on the
electronic and phonon properties of low-buckled silicene and germanene. With an
increase of the biaxial strain, the conduction bands at the high symmetric
$\Gamma$ and $M$ points of the first Brillouin zone shift significantly towards
the Fermi level in both silicene and germanene. In contrast, the E-field
changes the band dispersions near the $\Gamma$ and open a small band gap at the
K point in silicene. We found that the field-induced gap opening in silicene
could be enhanced by a compressive strain while mitigated by a tensile strain.
This result highlights the tunability of the electronic structures of silicene
by combining the mechanical strain and the electric field.
