The biological extinction that occurred at the Permian-Triassic boundary represents the most extensive loss of species of any known event of the past 550 million years. There have been a wide variety of explanations offered for this extinction. In the present paper, a number of the more popular recent hypotheses are evaluated in terms of predictions that they make, or that they imply, concerning the global carbon cycle. For this purpose, a mass balance model is used that calculates atmospheric CO2 and oceanic delta13C as a function of time. Hypotheses considered include: (i) the release of massive amounts of CO2 from the ocean to the atmosphere resulting in mass poisoning; (ii) the release of large amounts of CO2 from volcanic degassing; (iii) the release of methane stored in methane hydrates; (iv) the decomposition and oxidation of dead organisms to CO2 after sudden mass mortality; and (v) the long-term reorganization of the global carbon cycle. The modeling indicates that measured short-term changes in delta13C at the boundary are best explained by methane release with mass mortality and volcanic degassing contributing in secondary roles. None of the processes result in excessively high levels of atmospheric CO2 if they occurred on time scales of more than about 1,000 years. The idea of poisoning by high levels of atmospheric CO2 depends on the absence of subthermocline calcium carbonate deposition during the latest Permian. The most far-reaching effect was found to be reorganization of the carbon cycle with major sedimentary burial of organic matter shifting from the land to the sea, resulting in less burial overall, decreased atmospheric O2, and higher atmospheric CO2 for the entire Triassic Period.