Engineering Physics Annotation << Back А.А. Vlasov is the author of not only Vlasov equation but also Landau damping Rukhadze A.A. The important results which were obtained by A.A. Vlasov in 1944 and published in 1945 in [1] are presented. The solution of initially problem of small perturbations of longitudinal field in collision less plasma is given. Using the model distribution function of electrons is shown that the small perturbations of longitudinal field are oscillating with plasma frequency and damping in time. Thus at least one year before than L.D. Landau [2] by A.A. Vlasov was obtained the collision less damping of plasma waves which is known as Landau damping. Key words: initial problem, Coshy problem, Vlasov equation, improper integral, Landau damping. Contacts: E-mail: rukh@fpl.gpi.ru Pp. 19-24.