N.V. Gritsienko, A.V. Latyshev, A.A. Yushkanov Landau's problem of degenerate plasma oscillations with specular - accommodative boundary conditions (143K, LaTeX 2e with 2 EPS Figures) ABSTRACT. In the present paper the linearized problem of plasma oscillations in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the plasma boundary are considered. Coefficients of continuous and discrete spectra of the problem are found, and electron distribution function on the plasma boundary and electric field are expressed in explicit form.