The wake has a strong influence on the aerodynamics of a helicopter rotor operating in various flight modes. An accurate prediction of its geometry is critical for an improved understanding of aerodynamic performance, vibration and acoustics characteristics. In this paper, a higher-order lifting-surface method is discussed that uses singularity elements having distributed vorticity to model the lifting surfaces and shed wakes, and applies it to the problem of computing the free-wake geometry of a helicopter rotor in forward flight. Such distributed vorticity elements allow the representation of a force-free wake-vortex sheet that does not suffer from numerical singularities and is numerically robust with regard to the wake roll-up behavior. In contrast with other free-wake methods that use discrete vortex filaments, the new method does not require the implementation of vortex core models etc. Using this new method, the distorted wake geometry of a rotor in forward flight are computed, along with the capability of accounting for the effect of inboard active devices on wake development, airloads and downwash distribution.