In most of fluid-structure interaction analysis in engineering systems, velocity of the fluid flow is assumed constant and deterministic as time passes, while in this study, the flow velocity is modeled as a random process. In this thesis the strain/inertia gradient theory and knudsen number are employed in order to consider the effects of nano-structure and nano-flow, respectively. In continuation, the Hamiltonian function, symplectic transformation, and polar conversion are utilized in order to reach a standard form. Now, by assuming a stationary Gaussian random process for the velocity of fluid flow, the stochastic averaging method is used. Then the drift and diffusion coefficients of Itô’s equations are calculated, and thereafter, the stability of second moment of vibration amplitude is investigated. In the sequel, the mean and standard deviation of vibration amplitude of system are obtained by solving the Fokker-Planck-Kolmogorov equation. In this thesis, the symplectic transformation is obtained by means of the Genetic algorithm, which is employed to decouple the equations of model, without the effects of perturbation on system and only the first-mode divergence instability has been studied due to ineffectiveness of this transformation for flow velocities greater than the critical velocity corresponding to divergence of the first mode. The results of the present study show that structural damping and mass per unit length of fluid are more effective in the stochastic instability analysis rather than the deterministic one. In addition, for non-zero values of spectral density, the strain/inertia gradient theory predicts a higher mean flow velocity rather than strain gradient theory. On the other hand, by enhancing the mean flow velocity, the maximum safe value of spectral density decreases for stability. In both deterministic and stochastic instability analysis considering slip regime for liquid fluid causes insignificant changes in unstable mean flow velocity, while noticing this effect for gas fluid causes a sharp decrease of unstable mean flow velocity. Keywords: Nanotube conveying fluid, Strain/inertia gradient theory, Slip flow regime, Stochastic flow velocity, Stochastic averaging method, Fokker-Planck-Kolmogorov equation