The well-known stepped-index representation for graded-core fibre analysis is extended to cover all aspects of fibre propagation on a rigorous electromagnetic basis. Calculations are implemented on a large digital computer system, and a new, very efficient formulation is used, so that the resulting program package turns out to be a very general and powerful tool for fibre description. It can be used to establish on a quantitative basis the merits and limitations of well-known approximate procedures (e.g., the WKBJ method) and, at the same time, to get considerably deeper insight into the exact mode pattern of the graded-core fibre than provided by existing approximations.