A machine is described for covering book covers and sealing envelopes or articles of various kind. The machine comprises a fixed lower base suitable for resting a sheet of flexible plastic material for an article to be covered, an upper part movable towards said base and a heatable blade accommodated in the upper part to execute soldering of the overlapped ends of the plastic material sheet along the article edges when the upper part is approached to the lower base. The machine comprises an electric motor, a control member accessible from the outside of the machine for operating the electric motor and movement transmission means acting on the sides of the upper part to induce, at every activation of the electric motor, movement of the upper part towards the lower base for executing the soldering of the ends of the plastic material sheet.