A new system for ground moling has been patented by the University of Aberdeen and licensed world-wide. This new system is based on vibro-impact dynamics and offers significant advantages over existing systems in terms of penetrative capability and reduced soil disturbance. This paper describes current research into the mathematical modelling of the system. Periodic response is required to achieve the optimal penetrating conditions for the ground moling process, as this results in reduced soil penetration resistance. Therefore, there is a practical need for a robust and efficient methodology to calculate periodic responses for a wide range of operational parameters. Due to the structural complexity of a real vibro-impact moling system, the dynamic response of an idealised impact oscillator has been investigated in the first instance. This paper presents a detailed study of periodic responses of the impact oscillator under harmonic forcing using the alternating frequency-time harmonic balance method. Recommendations of how to effectively adapt the alternating frequency-time harmonic balance method for a stiff impacting system are given. (C) 2000 Elsevier Science Ltd. All rights reserved.