Computational fluid dynamics (CFD) was applied to model industrial flares under low-Btu, low-flow rate conditions (stand-by mode). The modeled tests were conducted at the John Zink R&D facility in Tulsa, OK in September 2010, using propylene/Tulsa Natural Gas/nitrogen as vent gases under open-air conditions. This work focuses on CFD modeling using the EDC (Eddy Dissipation Concept) and PDF (Probability Density Function) models to predict the destruction and removal efficiency (DRE), combustion efficiency (CE), and speciated emissions with a reduced 50-species combustion mechanism. Generally, the EDC model underpredicts DRE/CE while the PDF model overpredicts DRE/CE, when compared with measurements. The sources of discrepancies and the challenges to the flare modeling in the stand-by mode are discussed. In view of the significant differences between the measured and modeled results, further investigations involving a better domain with a refined mesh, a different turbulence model, or a combination of EDC/PDF models are warranted.