Current models that describe the extension of fungal hyphae and development of a mycelium either do not describe the role of vesicles in hyphal extension or do not correctly describe the experimentally observed profile for distribution of vesicles along the hypha. The present work uses the n-tanks-in-series approach to develop a model for hyphal extension that describes the intracellular transport of nutrient to a sub-apical zone where vesicles are formed and then transported to the tip, where tip extension occurs. The model was calibrated using experimental data from the literature for the extension of reproductive aerial hyphae of three different fungi, and was able to describe different profiles involving acceleration and deceleration of the extension rate. A sensitivity analysis showed that the supply of nutrient to the sub-apical vesicle-producing zone is a key factor influencing the rate of extension of the hypha. Although this model was used to describe the extension of a single reproductive aerial hypha, the use of the n-tanks-in-series approach to representing the hypha means that the model has the flexibility to be extended to describe the growth of other types of hyphae and the branching of hyphae to form a complete mycelium.