Abstract Based on the strain gradient and Eringen’s piezoelasticity theories, wave propagation of an embedded double-walled boron nitride nanotube (DWBNNT) conveying fluid is investigated using Euler–Bernoulli beam model. The elastic medium is simulated by the Pasternak foundation. The van der Waals (vdW) forces between the inner and outer nanotubes are taken into account. Since, considering electro-mechanical coupling made the nonlinear motion equations, a numerical procedure is proposed to evaluate the upstream and downstream phase velocities. The results indicate that the effect of nonlinear terms in motion equations on the phase velocity cannot be neglected at lower wave numbers. Furthermore, the effect of fluid-conveying on wave propagation of the DWBNNT is significant at lower wave numbers.