A micromechanical stick-slip model was developed to characterize the damping response of single-walled carbon nanotube nanocomposites. Depending on the strength of the interfacial bonding and the extent of applied loading, the single-walled carbon nanotube embedded in the matrix may either completely stick to the matrix or partially slide relative to the matrix. The slippage in the interface, together with the contact friction, may lead to the energy dissipation of single-walled carbon nanotube nanocomposites. The effects of the aspect ratio of single-walled carbon nanotube, interfacial bonding strength, volume fraction of single-walled carbon nanotube, and interfacial friction on the damping behavior of single-walled carbon nanotube nanocomposites were accounted for in the micromechanical stick-slip model. In order to validate the analytical model, the energy dissipation was also evaluated using the finite element method. A cylindrical finite element method, with an embedded single-walled carbon nanotube, was developed where the stick-slip behavior of the interface between the single-walled carbon nanotube and surrounding matrix was characterized using a contact element. It was found that the energy dissipation obtained from the finite element analysis agrees with that derived from the micromechanical stick-slip model. Moreover, the energy dissipation may significantly increase, when the single-walled carbon nanotube slippage takes place. The increment of the energy dissipation could be attributed to the interfacial contact friction between the single-walled carbon nanotube and the surround matrix as well as the viscoelastic properties of the matrix materials.