Meso-structural models are presently in common use for analysis of the mechanical behaviour, damage evolution and failure of concrete. These are constructed either from XCT images, or in-silico, using statistical information about concrete’s meso-scale constituents. As a minimum, such mod- els include mortar and aggregates as separate phases, while more detailed versions consider the interfacial transition zones (ITZ) between mortar and aggregates, and voids. Analyses of given meso-structures vary further by different constitutive modelling of constituents, with past works focusing on parameters’ calibration using experiments with one loading condition - either tension or compression. Using a detailed meso-structure representation, this work proposes a novel combination of constitutive relations, involving con- crete damage plasticity (CDP) for mortar and cohesive zone behaviour for ITZ. CDP parameters are calibrated using both compression and tension ex- periments with mortar samples. ITZ parameters are calibrated by comparing simulated stress-strain curves and failure patterns with data from compres- sion and tension experiments with concrete samples. This process leads to constitutive relations, applicable to both loading conditions, which has not been demonstrated previously, but is essential to extending the modelling approach to complex stress states encountered in real engineering structures. After establishing the realism of the approach, parametric studies are conducted to investigate the effects of friction between loading plate and specimen, the mortar dilation angle, the ITZ cohesive stiffness, critical stresses, fracture energy and mix mode ratio. The results show that mortar plasticity is the dominant energy dissipation mechanism in both compression and tension, and its rate governs the localisation of damage. The effect of ITZ parameters on the tensile behaviour is found to be negligible. Their effect on the compressive behaviour is found to be limited, but sufficient to propose a set of parameters working for both conditions. Importantly, under both loadings the ITZ is found to control failure localisation into a macroscopic crack in combination with mortar plasticity and damage. Predicted stress-stain curves, damage evolution and macro-crack propagation are shown to be in very good agreement with the experimental observations. This justifies the use of the proposed experimental-modelling strategy for developing models for analysis of complex loading conditions.