A mechanical N -body approach provides together the derivation of screening effect and of Landau damping. It deals with a single realization of a one-component plasma whose electrons have a velocity dispersion (for a thermal plasma, there must be many particles in a Debye sphere, a volume whose radius is the Debye length). On using the linearized motion of the electrons in their own electric field, it yields an equation of the type E Φ Φ = S ,