A new correlation to calculate the solid stresses at the contact face between the pipe and the mud cake, for the case of differential pipe sticking (DPS), is developed. The proposed correlation takes into consideration the effect of setting (contact) time, thickness of mud cake, and viscosity of mud filtrate on the behavior of the solid stresscs. A good match is obtained between the present correlation,the measured values, and terzaghi trend for calculating the resulted solid stresses. This in turn leads to estimate the minimum force required to free the stuck pipe.