I construct a continuous time model of strategic default and provide a numerical algorithm that solves it. I compare the results and computation times to standard discrete time models of sovereign debt. The method proposed here is faster than discrete time computation methods while obtaining similar quantitative results. The few differences between the models can all be attributed to a feature in continuous time that is absent in discrete time, costly deleveraging. I solve three variants of the model. The first includes short term maturity bonds only and a constant risk-free interest rate. The second allows for stochastic fluctuations in the risk-free rate. Finally, I extend the model to allow for long term maturity bonds.