A numerical model for boil-up of superheated liquid following loss of containment and expansion of two-phase mixture into the atmosphere is proposed and applied to evaluation of blast effects of Boiling Liquid Expanding Vapor Explosions (BLEVEs). The model assumes that the mixture in the two-phase cloud stays in thermodynamic equilibrium during expansion, whereas the air in the atmosphere obeys the ideal gas law with constant ratio of specific heats. The boundary between the two-phase cloud and ambient atmosphere is considered as a moving contact surface. The problem is solved numerically in the axisymmetric framework. Sample calculations of expansion of a spherical volume of superheated liquid are carried out for pressure-liquefied propane. Pressure profiles demonstrating propagation of depressurization wave into the cloud are presented together with mass fractions of vapor in the mixture. Solutions obtained for two-phase systems are compared with those for single-phase compressed gas. Scaling of overpressures in physical explosions is discussed. Validation of the model is carried out by comparison of simulations carried out in a wide range of cloud masses with experimental data. Two-dimensional simulations demonstrating BLEVE blast waves from a bursting near-surface vessel are presented. (C) 2016 Elsevier Ltd. All rights reserved.