A working process of a machine for wrapping products in packages, carried out with a thermoplastic material film from a reel, the process comprising: reducing a transversal section of a hollow mandrel to be smaller than a transversal dimension of a bundle of products, positioning a sealing device in a position for sealing overlapped longitudinal edges of the film while forming a new tubular film casing, arranging two vertically mobile elements of a sealing and transversal cutting assembly in a closure position on the head portion of the new tubular film casing and on the tail portion of the tubular film casing of a finished package, and conveying the new tubular film casing away from the mandrel, and repeating the process so that the product placed inside the tubular casing by the mandrel is wrapped in a tight adherent manner due to the elastic retraction of the film.