  We consider the two planes at zero temperature with isotropic conductivity
that are in relative lateral motion with velocity $v$ and inter-plane distance
$a$. Two models of conductivity are taken into account -- the constant and
frequency-dependent Drude models. The normal (perpendicular to planes) Casimir
force is analysed in detail for two systems -- i) two planes with identical
conductivity and ii) one of the planes is a perfect metal. The velocity
correction to the Casimir energy $\Delta_v\mathcal{E} \sim v^2$ for small
velocity for all considered cases. In the case of the constant conductivity
$\eta$, the energy correction is $ \Delta_v\mathcal{E} \sim \frac{\eta}{a^3}
\left(\frac{v}{\eta}\right)^2$for $v\ll \eta \ll 1$.
