In this study, low temperature Organic Rankine Cycle (ORC) systems with single and two-stage turbine are proposed for the production of electricity. The refrigerant R-134a is selected as working fluid based on peak temperature of the cycle for solar and geothermal applications. The design criteria of ORC system is introduced and explained in detail. The radial inflow turbine is selected to satisfy the design requirements. The cycle performance is taken as a key point in the design criteria. The system performance map is constructed based on both velocity triangles and approximate efficiency of turbine. The procedures for turbine and cycle design are introduced in detail. The components of cycle and turbine are modeled using baseline correlations via real gas tables and macros created on Excel for the refrigerant, R134a. Finally, the turbine geometry is optimized to attain maximum turbine efficiency via MATLAB optimization toolbox.