A simplified mathematical model representing the dynamic response of a tank containing a pressurized liquefied gas exposed to an external heat source, is presented. This scenario is of great practical interest in the process industry because it can result in the catastrophic failure of the tank with the explosive vaporization of the stored material (Boiling-Liquid Expanding-Vapour Explosion, BLEVE). The model has been validated against experimental data available in the literature and then applied to a number of reference cases, to assess the influence of the main parameters involved in the phenomenon on the evolution of the accident. This approach can be very helpful in various applications, such as risk analysis, where a large number of different scenarios must be simulated and/or the most critical conditions must be quickly identified. It has been found that the temperature of the tank wall in contact with the vapour phase is the most critical parameter. The time-to-failure of the tank is mainly affected by the received heat flux, while the time for the first opening of the pressure relief valve is very sensitive to both the initial storage temperature conditions and the heat input. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.