The increasing demand for exploration of deepwater reservoirs poses significant challenges for operators, well planners, and drilling engineers. As a recently developed deepwater drilling technology, riserless drilling offers numerous advantages over traditional riser-based drilling. However, riserless drilling is accompanied by substantial operational challenges, one of which is buckling of drillstrings. Buckling failure occurs when the drillstring misses an existing wellhead or experiences excessive torque and drag inside the near-surface section of a well. Buckling could also take place when a pilot well is being drilled and the weight-on-bit (WOB) limit is exceeded. In the absence of constraint from a riser, this buckling can give rise to catastrophic failure. Deep water allows for enough of the bottomhole assembly (BHA) to be exposed to reach the critical load for buckling. Classical buckling models cannot be applied to this situation because the force varies along the length of the assembly. To determine the operational limits and eliminate the risk of buckling-induced failures, a method for buckling analysis of a riserless drillstring has been developed. It is based on the finite element method, and the drillstring is modeled with a number of beams. The method can be utilized to predict the bending moment distribution along the drillstring, which can then be used to determine the critical buckling conditions. A case study is considered on a field failure, where a threaded connection on a riserless drilling BHA failed due to excessive bending. The predicted location of failure agrees with the field observation. The results can readily be extended to other BHAs.