The prediction and testing of formation pressure before and during drilling have not been well completed in highly overpressured areas all over the world. In such areas, serious drilling damages may result from the high overpressures existing in permeable sandy formations, but, unfortunately, the prediction methods commonly used are based on the lithological or physical changes measured within the low permeable shale neighbours! It is believed that high pore pressures must be generated in low permeable shales, which in turn transmit into the sandy formations. The discussion in this paper shows that the high pressures in sandy formations may be generated by other mechanisms and the role of the shales may be only a seal. The pressuring mechanisms in sandy formations may be classified into three types: the self-source type, neighbour-source type and allo-source type. The damage and predictability of the overpressures are discussed. Generally, the allo-source type high pressures may easily cause serious problems but are too difficult to be predicted. After analysing the defects of currently-used methods, some ideas of the prediction and testing of pressures are proposed.