Modelling elastic filament dynamics is a topic of high interest due to the wide range of applications. However, it has reached a high level of complexity in the literature, making it unaccessible to a beginner. In this paper we explain the main steps involved in the computational modelling of the dynamics of an elastic filament. We first derive equations governing the dynamics of an elastic lament suitable for a computer simulation implementation. The derivation starts from the relation between forces and potential energy in conservative systems in order to derive the equation of motion of any bead in the filament. Only two-dimensional movements are considered, but extensions to three dimensions can follow similar lines. Suggestions for computer implementations are provided in Matlab as well as an example of application related to the generation of musical sounds. This example allows a critical analysis of the numerical results obtained using a cross-disciplinary perspective. Since derivations start from basic physics equations, use simple calculus and computational implementations are straightforward, this paper proposes a different approach to introduce simple molecular dynamics simulations or animations of real systems in undergraduate elasticity or computer modelling courses. (Contains 5 figures.)