In this article, we develop an endogenous growth model to analyze the relation be- tween tax evasion and public debt accumulation. Our results are twofold. First, we find multiple equilibria where we find a positive (resp. negative) relation between tax evasion and public debt accumulation (resp. growth) in the neighborhood of the high BGP and a U-shaped (resp. inverted U-shaped) relation between tax evasion and public debt accumulation (resp. growth) in the neighborhood of the low BGP. Second, we show that the high BGP is saddle-path stable and the stability of the low BGP depends on the parameters of model : it can either be saddle-path stable (well determined), unstable (over determined) and in some cases, a Hopf bifurcation can appear.