Generating an object-oriented, geometric digital twin of an existing railway from its Point Cloud Data (PCD) is a laborious task, needing ten times more labour hours than scanning the physical asset. The resulting modelling cost counteracts the expected benefits of the twin. This cost and effort can be reduced by automating the process of creating such models. The first perceived challenge to achieving such automation is detecting masts from air-borne LiDAR data, as their position and function (separating substructure from superstructure) is critical to the subsequent detection of other elements. This paper presents a method that tackles the challenge above by leveraging the highly regulated and standardised nature of railways. In railway infrastructure, the geometric relations of a unit contain Overhead Line Equipment (OLE) between two mast pairs are consistent and repetitive throughout the track. Our method starts with tools for cleaning the PCD and roughly detecting its positioning and orientation. The resulting datasets are then processed by restricting the search region of the masts considering its positions compared to track centreline. Subsequently, the masts are detected using Random Sample Consensus (RANSAC) algorithm. The final deliverables of the method include the coordinates of the mast positions, detected point clusters and Three-Dimensional (3D) models of the masts in Industry Foundation Classes (IFC) format. We implemented the method in a prototype and tested it on three railway PCDs with a cumulative length of 18 km. The results indicated that the method achieves an overall detection rate of 94%. This is the first method in automatically detecting masts from air-borne LiDAR data.