This paper proposes an optional syllabus for the students in the XIIth grade. The proposed theme analyzes the concept of "variable mass" both in terms of classical mechanics and relativistic mechanics. In terms of classical mechanics we refer to the slow motion of a body, whose mass ranges in ascending way (by annealing a mass particle "dm" of the external environment to the mass body "m," within an elementary time interval "dt,") or in descending way (by detaching a mass particle "dm" from the mass body m within a time interval "dt"). If the theory of relativity, the body mass varies with speed and the body neither captures nor loses substance. Particular attention was paid to the analysis and synthesis of the physical phenomena involved and to their concrete applications.