Numerical modeling of the evolution, behavior, and combustion of two-phase hydrocarbon clouds released into the open atmosphere is presented. A Eulerian-Lagrangian model for transient flows of fuel vapor-droplet mixtures is formulated taking into account heat, mass, and momentum exchange between the gaseous and dispersed phases, soot formation, and radiative heat transfer. The calculations are performed for releases of pressure-liquefied propane; the total mass of fuel released varied in a wide range from 1 g up to 1000 kg and prerelease temperature 268-351 K. Formation and evolution of a two-phase cloud following a short-duration release of pressure-liquefied gas is first considered without ignition. Parameter ranges corresponding to mixing controlled and diffusion-controlled regimes of evaporation are obtained. The time for total evaporation of liquid fuel droplets is determined and the structure of the cloud is analyzed. Fireball development upon ignition of the fuel cloud is studied and the main stages of its evolution from reaction initiation until total fuel burnout are considered in detail. The calculated fireball shape and dynamics of ascent are shown to correlate quite well with the data from the Hasegawa-Sato experiments. The role of scale effects is studied by comparing the structure and gross characteristics of fireballs calculated for different fuel masses and storage conditions. The calculated dependence of the nondimensional fireball burning time on the Froude number agrees well with the experimental data. Radiation field distributions in fireballs of different scales are obtained and differences between optically thin and thick clouds are demonstrated. The radiative fraction of total combustion energy is shown to correlate well with available experimental data on turbulent propane flames.