As nuclear fusion progresses towards a sustainable energy source and the power of tokamak devices increases, a greater understanding of the radiation fields will be required. As well as on-load radiation fields, off-load or shutdown radiation field are an important consideration for the safety and economic viability of a commercial fusion reactor. Previously codes such as MCR2S have been written in order to predict the shutdown dose rates within, and in regions surrounding, a fusion reactor. MCR2S utilises a Constructive Solid Geometry (CSG) model and a superimposed structured mesh to calculate 3-D maps of the shutdown dose rate. A new approach to MCR2S calculations is proposed and implemented using a single unstructured mesh to replace both the CSG model and the superimposed structured mesh. This new MCR2S approach has been demonstrated on three models of increasing complexity. These models were: a sphere, the ITER computational shutdown dose rate benchmark and the DEMO computational shutdown dose rate benchmark. In each case the results were compared to MCR2S calculations performed using MCR2S with CSG geometry and a superimposed structured mesh. It was concluded that the results from the unstructured mesh implementation of MCR2S compared well to the CSG structured mesh calculations. It was found that the resolution of the unstructured mesh can significantly affect the results of the calculations, and therefore it is important to finely mesh components which contribute to the dose rate in the areas of interest. Although computationally more expensive it was found that there are some clear advantages when using unstructured meshes with MCR2S calculations which are outlined in this paper.