One of the central problems of a collapse hazard evaluation is the answer to the question: at what point on a collapse-prone site will a future collapse sink be located? If we have information about underground cavities, which can be the reason for a collapse, this problem may be solved fairly easily; otherwise, prediction is more difficult. This paper describes an approach to define the most probable location of a collapse at the stage of preparation for this event. The situation when we assume the presence of underground cavities, but have no exact information about them, is considered. This is typical for karst regions or for piping events. The approach includes the mathematical analysis of data from cone penetration tests or dynamic probing tests, carried out during standard site investigation. The basic principle is the recognized correspondence between the spatial distribution of these test data and the stress distribution in soils above an underground cavity. The results of practical application of this approach are given for some examples in Russia. In particular, in the city of Dzerzhinsk (near Nizhniy Novgorod) the forecast was completely confirmed, when inside a hazardous zone delineated in 1994 a collapse sink of karst origin was formed in 1996.