Purpose The purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids. Design/methodology/approach Considering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated. Findings The results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory. Originality/value This paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.