Due to the importance of investigating the vibrational behavior of carbon nanotubes, extensive research has been conducted in this field. In the present study, the natural frequencies of free vibrations of Single-Walled-Nanotube embedded in an elastic Winkler-Pasternak foundation are analyzed using a thin shell model and nonlocal elasticity theory. The governing equations of motion are derived based on Love’s shell theory and Hamilton’s principle. Since classical elasticity theory does not account for small-scale effects in the analysis of nanoscale structures—which can lead to inaccuracies in prediction—the Eringen's nonlocal elasticity theory is employed for more accurate modeling. The governing equations are discretized using the extended differential quadrature method and converted into an eigenvalue problem. Natural frequencies for various longitudinal and circumferential vibration modes are then computed. The predicted frequencies are compared with available data in the literature to validate the model. Furthermore, in the numerical results section, the effects of various parameters such as the length-to-radius ratio, radius-to-thickness ratio, properties of the elastic foundation, and the nonlocal parameter on the natural frequency of the carbon nanotube under different boundary conditions are analyzed and reported.