This paper presents a geometrical modelling principle for the modelling of yarns at the fibre level. The woven and the knitted textile structures are built of yarns, which on the other side, are fibrous assemblies. In many yarn and fabric modelling works, yarns are considered as a single line element; however, most yarns are composed of a number of staple or filament fibres. It is then very important to understand the yarn at the micro level for a better understanding, production and application of the above structures. The current paper aims to present the modelling and implementation of yarn structures at the fibre level using the algorithmic geometrical modelling principle. The research work uses basic assumptions for the building of the models and various implementation issues, connected with the proper representation of the single multi-filament yarns, plied yarns and finally the staple fibre yarns. Except for visualization, the generated yarn models are prepared as a basis for mechanical, thermal, fluid flow and other simulations of textile structures using FEM, CFD and other numerical tools.