In this work, the elastic properties of melts of polycarbonate (PC)/multi-wall carbon nanotubes (MWCNT) composites were studied by means of rotational and capillary rheometry. Linear viscoelastic shear oscillations combined with simultaneous electrical measurements, creep recovery experiments in shear and extrudate swell measurements were performed. The application of the fractional Zener model for the phenomenological description of the viscoelastic properties of PC/MWCNT composites in the linear regime is discussed. The modulus of the spring of the fractional Zener model is a measure of elasticity and increases with carbon nanotubes concentration. The results of creep recovery experiments reveal that the microstructure strongly influenced the viscosity and the reversible deformation of the nanocomposites. Below the rheological percolation threshold, agglomeration of carbon nanotubes generally led to an increase of the reversible deformation up to a maximum value. Above the rheological percolation threshold, a larger concentration of carbon nanotubes caused a decrease of the recoverable deformation. As revealed by capillary rheometry, the extrudate swell of the PC/MWCNT composites at shear rates above 100 s (-aEuro parts per thousand 1) was lower than the extrudate swell of neat polycarbonate which indicates the decrease of reversible deformation caused by the addition of MWCNT in capillary flows (large stress regime). The experimental data are discussed in the context of the current understanding of the rheological properties and the microstructure of polymer composites with carbon nanotubes.