Interfaces of fluid-fluid systems play an important role in the stability of foams and emulsions in chemistry, biology, consumer products, and foods. For most applications, surface active agents are added and adsorbed onto the interface to enhance stability, making the rheological behavior of the interface more complex. To understand the phenomena of these complex interfaces, various techniques are used to determine the interfacial properties. One of the most popular methods is the pendant drop technique. From the equilibrium state of the pendant drop, the interfacial tension of a system can be obtained quite easily in the absence of surface active agents. But when complex viscoelastic interfacial characteristics are considered, in particular in oscillatory measurements, interfacial constitutive relations need to be defined. Interfaces containing proteins, particles or Langmuir monolayers formed by insoluble low weight surfactants appear to act like viscoelastic solid membranes. In this work, a two-dimensional axisymmetric finite element model is designed to study the behavior of complex interfaces in pendant drop experiments. The bulk fluid consists of a Newtonian fluid, while the interface behaves according to the Kelvin-Voigt model as elastic interfacial forces dominate. To be able to capture large deformations, the Kelvin-Voigt constitutive model is made quasi-linear by using a combination of two non-linear strain tensors. A parameter study is performed to investigate the influence of the five model parameters of the quasi-linear Kelvin-Voigt equation. To demonstrate the applicability of the numerical model, a small amplitude oscillatory measurement is simulated.