Nowadays, destructive environmental forces such as earthquakes, tsunamis and winds accompanied with landslides, have mobilized the minds of the civil engineering communities around the world for finding new and better means for the protection of structures. As it is well known already, the conventional design approach, requires, that the structures passively resist environmental disturbances through a combination of strength, deformability and energy dissipation. Our experience shows that this is neither sufficient nor satisfactory. The basic role of passive energy dissipation devices when incorporated into a structure is to absorb or consume a portion of the input energy, thereby reducing energy dissipation demand on the primary structural members and minimizing possible structural damage. This paper represents an effort to strengthen the structural engineer’s interest on the problem of our modern times:passive energy dissipation. A number of these devices have been currently installed in structures throughout the world or is under testing. In this paper we have approached one of them: Tuned Mass Damper (TMD).