The Smoothed Particle Hydrodynamics method (SPH) is a meshfree Lagrangian simulation method widely applied for fluid simulations due to the advantages presented by this method for solving problems with free and deformable surfaces. In many scientific and engineering applications, surface tension forces play an important or even dominating role in the dynamics of the system. For instance, the breakage (instability) of a liquid jet or film is strongly affected by the strength of the surface tension at the liquid-air interface. Simulating deforming phase interfaces with strong topological changes is still today a challenging task. As a promising numerical method, here we use SPH to predict the interface instability at a water-air interface. With SPH, the main challenge in modelling surface tension at a free-surface is the accurate description of the interface (normal direction and curvature). When only the liquid phase is modelled (to decrease the computational cost), the standard SPH approximations to calculate the normal direction and curvature of the interface suffer from a lacking “full support”, i.e. the omitted and therefore missing gas particles. Various models for such free surface surface tension corrections were presented, see e.g. among others Sirotkin et al., Ordoubadi et al. or Ehigiamusoe et al. Many of these models follow the classical Continuum Surface Force (CSF) approach (Morris, Adami et al.) and incorporate different corrections/treatments at the surface. The objective of our ongoing study is to investigate the influence of different interface descriptions. We compare different free surface particle detection schemes, normal vector calculations and curvature estimations for the quality of the resulting surface-tension effect. In this work, we focus on two-dimensional problems and consider a static drop and oscillating drops as test cases.