The Herschel-Quincke (HQ) tube concept is well known for attenuation of plane-wave noise in ducts. However the HQ-tubes system can also be effectively applied to more complex duct sound fields due to higher-order modes. In this paper, an analytical technique is developed to model and predict the effects of HQ waveguides in three-dimensional ducts in which higher-order modes exist. The analytical technique involves modeling the waveguide-duct interfaces as finite piston sources that couple the acoustic field inside the main duct with the acoustic field within the HQ waveguides. The analytical model is used to provide insight into the attenuation mechanisms of the HQ waveguide arrays. The effects of the configuration and number of the HQ waveguides on the performance of the system are investigated. The analytical results are also validated on the inlet of a turbofan engine experimentally. The results demonstrate the potential of the HQ tube concept to reduce noise in ducts in many industrial applications where higher-order modes exist.