A method for characterisation of materials subjected to large strains beyond the levels when plastic instability occurs in standard tension tests is presented. Thin sheets of two types of hot-rolled steel are subjected to tension loading until fracture occurs. The deformation process is captured with a digital camera and by digital speckle photography (DSP) in-plane pointwise displacement fields are obtained. By numerical differentiation and assuming plastic incompressibility the equivalent plastic strain is determined. The characterisation performed in this paper consists of estimating material parameters in two constitutive models. These models are a piecewise linear plasticity model and a parabolic hardening model. By using inverse modelling including finite element analyses (FEA) of the tension tests the material parameters are adjusted to achieve a minimum in a so-called objective function. The objective function is basically a least-square functional based on the difference between the experimental and FE-calculated displacement and strain fields. Due to the large deformations an adaptive meshing technique is used in order to avoid highly distorted elements. The DSP- technique provided measurements, where the uncertainty of the equivalent plastic strain varied between 0.0015 and 0.0056. The maximum obtained strain was approximately 0.8. The true stress-strain curves based on the estimated parameters are validated in the low strain region by comparison with curves from standard tension tests