Abstarct: This research deals with the underbalanced drilling method which is one of the techniques used in the oil and gas industry. Underbalanced drilling occurs when the drilling fluid column has a lower pressure than the formation fluid, causing the formation fluid to get into the well and the drilling fluid to not loss. It is primarily used in reservoirs with low formation pressures. Due to the fact that many of Iran's oil reservoirs are depleting and dropping in pressure, this drilling method can be efficient and cause the least amount of damage to the reservoirs. There was a brief explanation of all types of drilling methods in this study, as well as a detailed explanation of the underbalanced drilling method. Also, possible problems as well as advantages of this method were examined. As a result, the wellbore stability is the main concern that needs to be investigated carefully. Having described the types of instability, we examined the parameters that affect instability, which combination of well logs and experimental relationships was used to calculate these parameters. The wellbore stability is modeled using FLAC2D software, a limited-scale numerical program limited to oil wells. Following the input of data and modeling of the well, the plastic zone around the wellbore is calculated and used to analyze the wellbore's stability using the normalized yield zone area method (NYZA). To obtain the initial cross section of the well, the normalized substrate level is divided by the area of the plastic region (breakage) around the wellbore. As a final step, the optimal mud pressure for underbalanced drilling in the examined fields has been determined and estimated using the NYZA method.