The intracellular signalling network of the p53 protein plays important roles in the genome protection and the control of cell cycle phase transitions. Recently observed oscillatory behaviour in single cells under stress conditions inspires several research groups in simulating and studying the dynamics of the protein with the perspective of a proper understanding of physiological meanings of the oscillations. We propose compartmental ODE and PDE models of p53 activation and regulation in single cells following DNA damage and we show that the p53 oscillations can be retrieved by plainly involving p53-Mdm2 and ATM-p53-Wip1 negative feedbacks, which are sufficient for oscillations experimentally, with no further need to introduce any delays into the protein responses and without considering additional positive feedback.