Power plant studies using systems codes allow the optimisation of designs to maximise or minimise some figure of merit: fusion power gain or cost of electricity, for example. The code should trade off between parameters to find the optimum whilst producing a solution consistent with physics and technology limitations. This paper describes the recently updated superconducting toroidal field coil (TFC) stress model in the systems code PROCESS. The TFC structure is critical in determining the reactor design as it influences key parameters, in particular the radial build and toroidal field. The model was validated with FEA and used to investigate how TF stress influences DEMO concept design in both pulsed (DEMO1) and steady-state (DEMO2) devices. The allowable stress in the TFC structural components was scanned between 440720 MPa for runs in which PROCESS was minimising the major radius, R0, and produced a variation in R0 of ?1 m for fixed aspect ratio. The capital cost varied by $23 bn over the same range. Understanding how some parameters limit the design is essential for exploring new DEMO concepts and guiding future research.