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Pre-drill prediction of formation pore pressure and pressure detection while drilling to recognize deviations from the expected pressure are important inputs for well planning and operational decision making. A method is proposed to determine pore pressure from a combination of downhole drilling mechanics parameters and in-situ rock and stress data using the concept of mechanical specific energy (MSE) and drilling efficiency (DE). This pore pressure estimation method (termed "DEMSE") is based on the theory that energy spent at the bit to remove a volume of rock is a function of the differential pressure (wellbore pressure minus pore pressure) that the rock is subjected to during drilling. A workflow is provided that illustrates the steps required to estimate pore pressure from drilling parameters and rock/stress data using DEMSE method. Pore pressure estimated from the DEMSE method is compared with a pore pressure estimate using a conventional sonic log based empirical technique for a deep water well in the Gulf of Mexico. Pore pressure estimates from the DEMSE method generally agree in magnitude and trend with the pressure estimates derived from sonic log data. The results of the DEMSE method have also been compared with pore pressure estimates from the classical d-exponent (dXc) methodology. Unlike the d-exponent methodology, which is an empirical correlation that considers only weight on bit (WOB), DEMSE is an energy based approach that takes into account both torque and WOB. Moreover, the normal compaction trendline (NCT) used in the DEMSE method can be correlated to a normal compaction porosity trendline; the same NCT used as a basis for conventional log-based pore pressure estimates. This gives the DEMSE method a significant advantage over the dXc method, in terms of predictive capability, by reducing the subjectivity that is involved in dXc-based pore pressure estimates. Finally, the importance of using downhole vs. surface data for pore pressure estimation purposes, specifically torque measurements at the bit, is illustrated through a field example. These findings suggest that downhole drilling mechanics data, when properly utilized, can provide reliable independent estimates of pore pressure in real-time at the bit, and for post well analysis to assist with constructing pore pressure forecasts.