This project presents a new model to consider the thermal effects, Pasternak shear foundation, transverse shear deformation and rotary inertia on vibration analysis of a single-walled carbon nanotube. Nonlocal elasticity theory is implemented to investigate the small-size effect on thermal vibration response of an embedded carbon nanotube. Based on Hamilton’s principle, the governing equations are derived and then solved analytically, in order to determine the nonlocal natural frequencies. Then, finite element analysis is employed to solve the frequency equations. Also, six different cases are reviewed in order to consider the various parameters. Results show that unlike the Pasternak foundation, the influence of Winkler constant on nonlocal frequency is negligible for low temperature changes. Moreover, the nonlocal frequencies are always smaller as compared with their local counterparts. In addition, in high shear modulus along with increase in aspect ratio, the nonlocal frequency decreases. Furthermore, the thermal vibration analysis of a short single-walled carbon nanotubes embedded in an elastic medium based on nonlocal Timoshenko beam model is considered in this study. Analytical solution was used to solve the constitutive equations. A Winkler- and Pasternak type foundation is employed to model the interaction of short carbon nanotube and surrounding elastic medium. Influence of all parameter such as nonlocal small-scale effects, high temperature changes, Winkler modulus parameter, Pasternak shear parameter, vibration mode and aspect ratio of short carbon nanotubes on the natural frequency are analyzed and discussed. The present study shows that for high temperature changes, the effect of Winkler constant in different nonlocal parameters on natural frequency is negligible. In addition, for all temperatures, the nonlocal frequency, like the previous case, are always smaller than the local counterparts. Furthermore, for high Pasternak modulus, by increasing the aspect ratio, the nonlocal frequency decreases. It is concluded that short carbon nanotubes have the higher frequencies as compared with long nanotubes. For short carbon nanotubes, by increasing the temperature change, in a constant nonlocal parameter, the natural frequencies increase. Generally, it is concluded that the effect of Pasternak foundation on natural frequency is more significant as compared with the effects of thermal loading, Winkler modulus and nonlocal parameter and should be considered in vibration analysis of short carbon nanotubes. Finally, it should be noted that the rotary inertia, nonlocal parameter, and thermal loading have the effect of reducing natural frequency in the case of high temperature changes for long single-walled carbon nanotubes. Keywords: Nonlocal elasticity theory; Carbon nanotubes; Pasternak Foundation; Finite element method.