The design of radial compressor inlets for transonic ow is examined. A theoretical model [1] quanti es the losses in the tip sections caused by the choke margin (incidence) and the blockage of the blades. It identi es clear design rules for the tip sections: to achieve the highest ef ciency, these require minimum blockage (low blade thickness and splitter vanes) and low choke margin (close to the uniqueincidence condition). Simulations of the NASA rotor 37 transonic axial compressor (with CFX-TASC ow) are used to validate the use of three-dimensional viscous computational uid dynamics (CFD) for transonic compressor inlets and to demonstrate that the key performance features suggested by the simple model are also modelled in three-dimensional viscous ow simulations. The simple model together with CFD simulations has been used for the design of tip sections at the inlet of a transonic radial compressor. CFD simulations were used to select the position of the shock to give a low choke margin, to reduce the preshock Mach number and also to optimize the shape and position of the leading edge of the splitter vanes.