We consider the two planes 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 model. 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 \(v\ll \eta \ll 1\).