The development of rare-earth barium copper oxide (REBCO) coated conductors with an extremely high critical current density under ultra-high fields opens up a high-field path towards large-scale fusion. The latest technology has inspired cable-in-conduit conductors (CICC) such as conductor on round core (CORC) wires, twisted stacked tape conductor (TSTC) cables and Rutherford cables with outstanding current-carrying capacities. In order to realise an inductance balance and decrease magnetic diffusion, these cables have been twisted or folded to a certain extent, thus breaking the mechanical behaviour of the ceramic superconductor and limiting their potential for ultra-high-field applications. One possible solution is to employ a non-twisted cable, which offers maximum protection of its mechanical properties and enables a parallel orientation of the toroidal field vector to the surface of REBCO coated conductors. However, the applied physics community’s attitude towards using non-twisted, parallel REBCO stacked-tape cables is one of scepticism, the main argument being that the nonlinear E-J behaviour associated with screening current in the parallel stack might lead to a field distortion and reduce the performance of superconductivity. Recent analyses have demonstrated that the effect of screening current decreases significantly owing to a wavelike magnetic field distribution along the cable. The authors obtained similar results using H-formulation and T-A formulation based finite element methods and demonstrated that the non-twisted cable may be feasible for DC current transmission toroidal field coils in magnetic-confinement devices. Furthermore, the electromechanical behaviour of toroidal field coils has been evaluated via the Maxwell stress, solved by using an A-V formulation. It was discovered that the stress generated by the toroidal field coils is within the stress tolerance of the REBCO coated conductor, something which is of great significance in promoting the application of REBCO coated conductors for ultra-high-field magnetic-confinement plasma devices.