In shear or dilational testing, the interfacial rheology of a protein film adsorbed at a fluid–fluid interface is often determined by its response to dynamic deformation. In order to extract characterising parameters from the response data, a model must be assumed in order to fit the response, yet the assumption is difficult to validate due to the limited strain range accessible by most instruments. In this work, a modelling approach was developed to extract characterising parameters from stress–strain curves measured in a high-strain extensional mode of deformation. This mode of testing is insensitive to interfacial tension gradients, making it particularly useful for the study of interfacially adsorbed materials, such as proteins, where the relationship between interfacial tension and interfacial rheology is complex. A four-parameter version of the Generalised Maxwell Model (GMM) for three-dimensional viscoelastic materials successfully describes the response of a two-dimensional β-lactoglobulin interfacial film over a full linear strain range of 0–100%. The GMM asserts that viscoelastic relaxation occurs on multiple timescales, and in this case the two associated time constants give new insights into the nature of interfacial rheology, and its dependence on mass transfer with the bulk solution. In particular, washing out protein from the bulk solution has little effect on the initial response of the system, but a significant effect on the larger-strain response. Fitting a smaller strain range with a less parameterised model (e.g. 0–5% strain fitted with 2 parameters, or 0–20% fitted with 3 parameters) yielded a result that was reasonable up to the strain rate fitted, although the model did not predict well the response to greater strains. The major consequence is that unless a strain range large enough to allow significant influence of viscosity on observed response is tested, unreliable values of viscosity may be determined. Three other common proteins (lysozyme, bovine serum albumin and β-casein) were also tested. In each case, the films showed viscoelastic behaviour that could be well described by the 4-parameter GMM, allowing the viscous components for these protein films to be estimated more accurately than has been possible to date.