The paper deals with the development of mathematical models for detailed simulation of lateral jet penetration into the fluidized bed (FB), primarily from the aspect of feeding of gaseous and liquid fuels into FB furnaces. For that purpose a series of comparisons has been performed between the results of in-house developed procedure- fluid-porous medium numerical simulation of gaseous jet penetration into the fluidized bed, Fluent?s two-fluid Euler-Euler FB simulation model, and experimental results (from the literature) of gaseous jet penetration into the 2D FB. The calculation results, using both models, and experimental data are in good agreement. The developed simulation procedures of jet penetration into the FB are applied to the analysis of the effects, which are registered during the experiments on a fluidized pilot furnace with feeding of liquid waste fuels into the bed, and brief description of the experiments is also presented in the paper. Registered effect suggests that the water in the fuel improved mixing of fuel and oxidizer in the FB furnace, by increasing jet penetration into the FB due to sudden evaporation of water at the entry into the furnace. In order to clarify this effect, numerical simulations of jet penetration into the FB with three-phase systems: gas (fuel, oxidizer, and water vapour), bed particles and water, have been carried out.