Structural evaluation of masonry against dynamic seismic actions invariably requires appropriate cyclic compression constitutive models. However, not many research studies have been dedicated to date to investigate the cyclic compression behaviour of masonry. Therefore, series of experimental investigation followed by analytical model verification were employed in this research to better understand the cyclic compression characteristics of masonry. Twelve masonry wallettes were experimentally tested under cyclic compression loading with different unit-to-mortar assemblies, which are commonly found in masonry structures. The experimental results indicated that the cyclic compression behaviour is greatly influenced by the masonry compressive strength and deformation properties. Thereafter, the ability of five literature analytical models to predict the masonry structural response under cyclic compression loading was investigated. The advantages and limitations of these models are presented and discussed, and the most appropriate analytical model to define the cyclic compression characteristics of masonry has been evaluated and reported. The suggested analytical model is shown to predict the cyclic compression characteristics of different masonry assemblies such as the envelop response, the stiffness degradation, the plastic strain history of the unloading and reloading stages.