Nanotechnology has great potential applications in many fields such as chemistry, physics, material science, etc. In the recent years, nanostructures due to their extraordinary properties are used in a wide range of nanodevices such as nanosensors, nanoactuators and nanocomposites. So, appropriate physical and mechanical analysis of these structures should be under investigation for proper design and useful handling of them. After the invention of carbon nanotubes a large number of researches, using experimental and theorical approaches, have been directed to analyze micro and nanostructures. Atomistic modelings are expensive for large-sized atomic systems and conducting experiments at the nanoscale are difficult and sometimes not applicable. Consequently, continuum models which are proposed may be used for a larger system while they are able to include nanoscale size effect. Since the Carbon nanotubes may have some defects which cause obvious changes in their behaviors. Geometrical imperfection is one type of these defects which may occur during CNTs manufacturing. Generally, this type of CNTs may be applied in a curved configuration in other nanostructures such as nanocomposites. In this case these nanotubes cannot be modeled as straight components. In the present work, stability and vibration of an embedded single walled carbon nanotube with small initial curvature under lateral loading has been investigated based on Eringen's nonlocal elasticity theory. Euler Bernoulli beam theory is used to model the behavior of nanotubes. Winkler-Pasternak type elastic foundation has been used to estimate the effect of matrix. Governing equations have been derived using the principle of virtual work. The relationship among critical buckling load, nonlocal parameter, and mode numbers are investigated by parametric studies. It has seen that nonlocal parameter contribute to the mechanical properties of nanostructures and should be considered. key word:nonlocal elasticity theory, nanoring, stability analysis, vibration.