Reconfigurable transfer lines (RTLs), which are highly responsive to demand fluctuations, have gained increasing attention. This research deals with the line configuration design and balancing problem of RTLs under uncertain demand where line configuration can be changed to satisfy a given demand with minimum cost. It is assumed that the demand of a single product is in interval form. Such RTL is composed of a sequence of workstations and each workstation consists of several identical CNC machining centres. The RTL production capability could be adjusted by adding/removing machines or overtime work. The line configuration and balancing decision is to determine the number of workstations, specify the set-up and the number of machines in each workstation, then assign operations to workstations with various constrains satisfied. Interval optimisation theory is introduced to cope with demand uncertainty. A two-stage optimisation model is developed to handle the primary RTL design and the necessary system reconfiguration. A heuristic algorithm based on greedy randomised adaptive search procedure combined with variable neighbourhood search is given for operation assignment. An industrial case study is carried out and multiple near-optimal solutions are obtained. The feasibility and effectiveness of the proposed method is verified by the comparison of computational experiments.