<p>This study investigates the natural frequencies of a flexible string moving axially within a fluid using an approximate analytical approach. The motion of such axially moving string or beam is governed by equations incorporating centripetal and Coriolis acceleration components. When these continua travel through a fluid, they are subjected to various fluid forces. Due to such forces, the spatially varying coefficients appear in the governing differential equation, which complicates the derivation of closed-form solutions. In this paper, these fluid forces are initially modeled as a distributed follower force with viscous damping. Approximate closed-form expressions for natural frequencies are derived using an asymptotic technique for an axially moving string subjected to a distributed follower force. This approach is further applied to determine the natural frequencies of the traveling string, accounting for all viscous fluid forces.</p>