Somitogenesis is a fundamental embryonic process in vertebrates, where the presomitic mesoderm (PSM) periodically segments into somites, the precursors of the vertebral column. This process resembles the Plateau-Rayleigh instability in liquid streams, where a cylindrical fluid breaks into droplets due to surface tension. However, existing fluid models neglect key features of somitogenesis, such as structural order and non-local viscoelasticity. To address this gap, we propose using the continuum theory of active gels, which incorporates these effects. Our model represents the PSM as a composite system: an inner bulk fluid phase that is enclosed by a two-dimensional nematic fluid layer. Due to its nematic alignment, this model exhibits a viscoelastic response to a mechanical stimulus. The external medium is described as an ideal fluid. The goal of this internship is to investigate the dynamics of the free boundary between the PSM and the external medium, focusing on small interfacial deformations. We will linearize the model and use asymptotic methods, such as linear stability analysis, to gain insights into the mechanisms destabilizing the PSM interface. This project is part of the ANR consortium Fidelio, which unites experimentalists and theoreticians from Institut Curie and Université de Lorraine. Regular collaboration with experimental teams will guide the theoretical work.