Physical and mathematical modelling techniques have been used to investigate the hydrodynamic significance of some aspects of the morphology of graptoloids. Functional structures are identified which could have had an impact on interpretations of graptolite taxonomy, oceanography and evolution. Experiments, testing isolated specimens in seawater and scale models in oil, show that the nema, cauda and virgula had a profound effect on the orientation of scandent graptoloids. These structures acted as trailing stabilisers, enforcing a stable orientation on the rest of the colony. Isolated monograptids with hooked and simple thecae have their orientation controlled by the nema, and would have presented their rhabdosomes to water sicula aperture first. This orientation control function was particularly marked in experiments on immature specimens, probably because these early growth stages are preserved with full length nemas. Oil tank modelling highlighted the importance of mass distribution for colony orientation, and observations of flow patterns over detailed models in a wind tunnel indicated that the increased surface area provided by secondary structures (e.g. vanes) further enforced this function. Mathematical modelling of distal structures such as the nema suggested that they would have functioned as stabilisers for all scandent graptoloids if they were of sufficient length or surface area (i.e. were thickened or bore vanes). The rate at which they would have acted to stabilise the colony was a function of this length or width and the distribution of colony mass, with longer or wider structures responding faster to changes in current orientation. The graptolite fossil record contains numerous examples of specimens bearing long virgulae and vane structures. Spines are a common feature of the proximal ends of biserial and uniserial scandent graptoloids. The virgella is evolutionarily conserved, while other processes have evolved more than once. Spines appear on the sicular aperture or on the first one or two thecae.