We present the analytical solution of a mathematical model to explain the growth kinetics of gold nanorods grown via seed mediated synthesis. In the synthesis process, pre-formed gold nanoseeds are added to a solution containing cylindrical surfactant micelles, gold salt and a reducing agent. A mechanism is proposed based on several control experiments to understand the role of each species. Surfactant micelles act as a template for one-dimensional growth and solubilize the gold salt; the reducing agent partially reduces gold salt and the seed particles auto-catalytically reduce the partially reduced salt into metallic atoms. Based on this mechanism a mathematical model has been developed. Our model based on this physically relevant mechanism shows a bound exponential growth of nanorod length. The analytical model captures quantitatively the growth curves obtained in our experiments and the kinetic data of others under different synthesis conditions reported in the literature. The model can be appropriately modified to explain the growth kinetics of other seed-mediated growth processes of metallic nanorods. © The Royal Society of Chemistry 2016.