This paper studies the relationship between firm export dynamics and financial constraints in a small open economy model. Robust findings in the literature show that new exporters begin by exporting very small quantities, with most of them exiting the foreign market soon after. However, those that survive expand very rapidly and are much less likely to exit. As reported by Ruhl and Willis (2008a), standard trade models with heterogeneous firms cannot replicate these facts. We add borrowing constraints to an otherwise standard model and calibrate it using microdata on export dynamics. We find that financial constraints can largely account for the decreasing hazard rate and the increasing export volume of new exporters. We then provide empirical evidence supporting this mechanism and study its implications for understanding the effects of a large devaluation on aggregate exports.