A one-dimensional computational model based on a finite difference scheme has been developed to model the transient formation of flammable atmospheres upon the diffusion of fuel vapor following the exposure of liquid fuel surfaces to air within containers at constant pressure. Two fuels were modeled, namely n-pentane and methanol. The effects of convection and temperature gradients produced by the extraction of the latent heat of evaporation from the liquid surface were taken into account. The thermodynamic and transport properties were taken to be variable. The model predictions for the variation with time of the location of the lean flammability limit concentration compared favorably with the corresponding experimental values. The width of the flammable region bounded between the lower and upper flammability limits concentrations was calculated for both fuels along with the associated temperature and concentration profiles. The role of ambient temperature on the formation of the flammable zone was also investigated and presented for different typical cases. The results show that a detailed parametric study is required individually for each fuel in order to assess the trends of the flammable regions development with changes in different operating parameters.