This paper presents a constitutive relationship to describe the uniaxial response in statics of brick and mortar samples of Adobe, a traditional masonry whose components are made of sundried soil mixture reinforced with fibres. Only recently Adobe has been attracting scientific attention, primarily as a consequence of the dramatic failures these structures have suffered in regions prone to earthquakes. Furthermore, it possesses eco-friendly material properties which are attractive features for western countries forced to reduce the environmental impact of modern building industry. Nevertheless, the mechanical properties of Adobe are still largely neglected, especially with regards to the influence of soil mixture components. The study of the structural performance of masonry starts from the assessment of the material performance of its components. Thus, an extensive characterization campaign was performed by Delft University of Technology and the Military Engineering Laboratory of the Netherlands. Three types of bricks and one type of mortar with different mixture components proportions, were subjected to granulometry, moisture content, density tests and uniaxial compressive and three point bending tests. Predictive formulations for compressive and tensile strength and deformation values have been proposed by the authors. These relations include the dependency of mixture components and moisture content. In this paper, constitutive laws are developed for Adobe in pure compression and tension validated by experimental results. In compression, the force-displacement curves were interpolated according to several existing constitutive laws and the model originally developed by Priestley for concrete masonry elements was finally selected as best fitting. Despite the differences in terms of mechanical parameters, the analytical assessment revealed that the experimental force-displacement graphs of all the different types of bricks could be interpolated using the same model with the same calibrating values. Furthermore, the uniaxial response in tension was derived according to an inverse approach. A numerical model recently developed by the authors and calibrated with respect to the compressive and bending tests was used to simulate uniaxial tensile tests. Also in tension, a common trend among types was observed. The results of the constitutive modelling frames components of Adobe within the class of quasi brittle (geo)materials, with particular reference to concrete. This paper presents the experimental results of the tested samples and the related analytical and numerical modelling.