DURING DRILLING OPERATIONS OF OIL AND GAS WELLS, PARTICULARLY IN UNDER BALANCED DRILLING, THE DRILLING MUD WEIGHT SHOULD BE CHOSEN IN A WAY SO THAT IT DOES NOT CAUSE INSTABILITY AND PROBLEMS ARISING FROM IT. TO DETERMINE THE OPTIMAL DRILLING MUD WEIGHT, IT IS NECESSARY TO HAVE ACCURATE ANALYSIS OF THE STRESSES ON THE WELLBORE AND THE EFFECT OF MUD WEIGHT ON THE AMOUNT AND DISTRIBUTING THESE STRESSES IN ORDER TO PREVENT INSTABILITY. WELLBORE INSTABILITY LEADS TO WASTING MUCH TIME AND MONEY IN ALL AROUND THE WORLD. THEREFORE, THE ANALYSIS AND PREDICTION OF THE WELLBORE STABILITY ARE UTMOST IMPORTANCE. TO ANALYZE THE STABILITY OF WELL, SOME SOFTWARE SUCH AS FLAC ARE COMMONLY USED WHICH ARE DESIGNED BASED ON NUMERICAL METHODS. IN THIS STUDY THE MINIMUM ALLOWABLE OF DRILLING MUD WEIGHT USING THE ANALYTICAL SOLUTION) IS DISCUSSED IN ONE OF THE FIELDS OF SOUTHWEST IRAN. TO DETERMINE THE MINIMUM ALLOWABLE OF DRILLING MUD WEIGHT, THE ANALYTICAL SOLUTION OF JOHN BRAY IS USED AND THEN USING DEFINITION OF NYZA, WHICH IS THE CROSS-SECTIONAL AREA OF THE YIELDED ROCK AROUND THE BOREHOLE DIVIDED BY THE AREA OF THE ORIGINAL BOREHOLE, IS PREDICTED IN ANALYTICAL METHOD.