The favorable energy-absorption properties of metal foams have been frequently proposed for damping or anti-crash applications. The aim of this paper is to investigate the endurance of these properties for composite structures, made by a metal or a hybrid metal-polymeric foam used as the core filling of a tubular metal case. The results of experimental tests are shown, run with two types of structures: 1) square steel tubes filled with aluminum or with hybrid aluminum-polymer foams; 2) round titanium tubes filled with aluminum foams. The paper shows that the damping properties of a foam-filled tube change (improve) with the number of cycles, while all other dynamic properties are nearly constant. This result is very important for several potential applications where damping is crucial, e.g., for machine tools.