Organic Rankine cycle technology is gaining increasing interest as one of potent future waste heat recovery potential from internal combustion engines. The turbine is the component where power production takes place. Therefore, careful attention to the turbine design through mathematical and numerical simulations is required. As the rotor is the main component of the turbine, the generation of the 3D shape of the rotor blades and stator vanes is of great importance. Although several types of commercial software have been developed, such types are still expensive and time-consuming. In this study, detailed mathematical modelling was presented. To account for real gas properties, REFPROP software was used. Moreover, a detailed 3D CFD numerical analysis was presented to examine the nature of the flow after generating the 3D shapes of the turbine. Moreover, finite element analysis was performed using various types of materials to obtain best-fit material for the current application. As the turbine is part of a larger system (i.e., ORC system), the effects of its performance on the whole ORC system were discussed. The results showed that the flow was smooth with no recirculation at the design point except at the last part of the suction surface where strong vortices were noticed. Despite the strong vortices, the mathematical model proved to be an effective and fast tool for the generation of the 3D shapes of turbine blades and vanes. The deviations between the 1D mean-line and 3D CFD in turbine efficiency and power output were 2.28% and 5.10%, respectively.