Abstract: Inspired by the locomotion of organisms at the micro-scale using appendages we derive a simplified model of a flagellum-like micro-swimmer. We study a passive one-dimensional elastic filament immersed in a viscous fluid driven by an external torque on the head of the filament based on models from the literature. We derive an elastohydrodynamic model describing the fluid-filament interaction. Using weakly non-linear analysis and numerical simulations we show that this simple model indeed can describe the propulsion of a filament. The model gives a non-zero and non-trivial swimming speed which depends only on two non-dimensional model-parameters, viscous drag anisotropy and a filament property parameter.