We report on a comprehensive computer simulation study of the liquid-crystal phase behaviour of purely repulsive, semi-flexible rod-like particles. For the four aspect ratios we consider, the particles form five distinct phases depending on their packing fraction and bending flexibility: the isotropic, nematic, smectic A, smectic B, and crystal phase. Upon increasing the particle bending flexibility, the various phase transitions shift to larger packing fractions. Increasing the aspect ratio achieves the opposite effect. We find two different ways in which the layer thickness of the particles in the smectic A phase may respond to an increase in concentration. The layer thickness may either decrease or increase depending on the aspect ratio ...