In this work, we show theoretical results of the behaviour of the extinction cross section as a function of the incident wavelength for metallic nanotubes (Nts) with a 2D core-shell structure. To calculate the optical response of the gold, silver and cooper system, an exact integral formalism is implemented. The method is based on Green's integral theorem, and it allows us to compute the electromagnetic field at any point in space. For a correct description of the constitutive parameters of the metallic shell, we introduce a corrective model for the dielectric function in terms of the shell thickness in the range 1 to 10 nm. In particular, we investigate the features of surface plasmons in metallic Nts, and in the cases of Au and Cu, the mechanisms of the interband transitions play a relevant role. In this paper, we show that a quasi-static approach is not sufficient to account the plasmon-plasmon interaction in Ag Nts. The aim of these studies is to characterize core size and shell thicknesses of the Nts by means of the surface plasmon resonance observed in the far field.