Prediction of abdominal viscera and tumour positions during free breathing is a major challenge from which several medical applications could benefit. For instance, in radiotherapy it would reduce the healthy tissue irradiation. In this paper, we present a new approach to predict real-time abdominal viscera positions during free breathing. Our method needs an abdo-thoracic 3D preoperative CT or MR image, a second one limited to the diaphragmatic area, and a tracking of the patient's skin position. First, a physical analysis of the breathing motion shows it is possible to predict accurately abdominal viscera positions from the skin position and a modelling of the diaphragm motion. Secondly, a quantitative analysis of the skin and organ motion allows us to define the demands our real-time simulation has to fulfill. Then, we present in detail all the necessary steps of our original method to compute a deformation field from data extracted in both 3D preoperative image and skin surface tracking. Finally, experiments carried out with two human data show that our simulation model predicts abdominal viscera positions, such as liver, kidneys or spleen, at 50 Hz with an accuracy within 2-3 mm.