The aim of the study is to determine the breaking point of Kenyan public debt through the use of Extreme Value Theorem (EVT). EVT focuses on the tail end of distributions to be able to identify maxima and minima points. With the rising debt levels since devolution, from Kenya Shillings (KES) 500 billion in 2013 to KES 2.5 trillion in 2015, and warnings from international bodies such as International Monetary Fund (IMF) and World Bank on rising debt levels, there is need to determine sustainability of debts beyond analyst speculations. The use of the special case of EVT known as Generalized Extreme Value (GEV) application looks at a degenerate distribution factor thus ensuring the tail end of the distribution, that is, the maxima converges to the GEV despite the distribution of the data set (no assumption on the distribution of the data set). From the study the Gumbel model was determined to be the most appropriate model and with a 95% threshold, the GEV projected total debt maxima to be KES 5 trillion. This is evidence that the current debt levels of KES 2.5 trillion is still sustainable but should however be monitored.