As a competitive small-scale turbomachinery option, Tesla turbines have wide potential in various fields, such as renewable energy generation systems and small power equipment. This paper investigates the influence of disc tip geometry, including its profile and relative height, on the aerodynamic performance and flow characteristics of one-to-one and one-to-many multichannel Tesla turbines. The results indicate that compared to the turbine with blunt tips, the isentropic efficiency of the one-to-one turbine with sharp tips has a little decrease, which is because the relative tangential velocity gradient near the rotational disc walls decreases a little and additional vortices are generated at the rotor inlet, while that of the one-to-many turbine with sharp tips increases significantly, resulting from an increase in the relative tangential velocity in the disc channels and a decrease in the low Mach number and vortex area; for instance the turbine efficiency for the former relatively decreases by 3.6% and that for the latter increases by 13.5% at 30,000 r/min. In addition, the isentropic efficiency of the one-to-many turbine with sharp tips goes up with increasing relative height due to increasing improvement of flow status, and its increment rate slows down. A circular or elliptic tip performs better with lower relative height and a triangular tip behaves better with higher relative height. To sum up, a blunt disc tip is recommended for the one-to-one turbine, and a sharp disc tip is for the one-to-many turbine. The relative height and tip profile of the one-to-many turbine should be determined according to their effects on turbine performance, manufacturing difficulty and mechanical deformation.