Constitutive models for masonry require a number of parameters to define material behaviour with sufficient accuracy. It is a common practice to determine such material parameters from the results of various, relatively simple, small-scale laboratory experiments. However, the effectiveness of determining material parameters that are representative of masonry from small scale experiments have found to be problematic. This paper investigates the material parameter identification problem for masonry constitutive models. The methodology is based on an inverse analysis containing an optimisation procedure and surrogate modelling. The general framework of the non-linear estimate methodology and the parameter identification problems are discussed.