This paper demonstrates how simulation of wellbore pressures during different blowout scenarios; borehole stability analysis and solids transport can be applied to the problem of blowout risk assessment. This is a technology area that previously has been overlooked by petroleum geomechanics practitioners. The proposed analysis methodology emphasizes the importance of understanding the transient evolution of the kick within the borehole, as this is a key factor in assessing whether bridging is likely to occur during the events leading up to a blowout. Three representative situations are analyzed and conditions leading to self-killing are reviewed. Analyses of a shallow-gas kick and blowout reproduce the numerous field observations that self-killing is likely from the combination several possible mechanisms - borehole collapse of soft shales, sand erosion leading to cavity collapse in the initially-overpressured aquifer zone, gas depressurization and brine influx. For deeper water scenarios a sudden failure of the marine riser while drilling-ahead is expected to result in conditions where self-killing occurs. The rapid reduction in wellbore hydrostatic pressure following the loss of the riser margin is considered sufficient to initiate borehole failure that causes a cavings-loading that chokes the hydrocarbon influx, so allowing settling of the entrained solids and plugging of the borehole. In contrast, a more slowly-evolving swabbed kick is not expected to be self-killing. Here the slow progression of borehole instability is not expected to impede the increasing kick flow-rate. It is hoped that by presenting these analyses the industry may become better informed of the geomechanical and borehole stability aspects of kicks and blowouts, and that as a consequence well designs in deep-water can become more robust and inherently safer