Large Eddy Simulations of atomization and evaporation of liquid fuel sprays in diesel engine conditions are performed with stochastic breakup and non-equilibrium droplet heat and mass transfer models. The size and number density of the droplets generated by the breakup model are assumed to be governed by a Fokker-Planck equation, describing the evolution of the PDF of droplet radii. The fragmentation intensity spectrum is considered to be Gaussian and the scale of Lagrangian relative velocity fluctuations is included in the breakup frequency calculations. The aerodynamic interactions of droplets in the dense part of the spray are modeled by correcting the relative velocity of droplets in the wake of other droplets. The stochastic breakup model is employed together with the wake interaction model for simulations of non-evaporating and evaporating sprays in various gas temperature and pressure conditions. The predicted results for physical spray parameters, such as the spray penetration length are found to be in good agreement with the available experimental data.