Abstract: The standard thin-wall approximation in Coleman-de Luccia (CdL) instanton is shown to fail at least in one modified model of gravity: the Eddington-inspired Born-Infeld (EiBI) theory. Here we apply the thin-wall approximation to the EiBI-scalar action and show that the resulting bounce gives negative-definite results even with the vanishing EiBI nonlinearity constant κ. In contrast, the full numerical thick-wall investigation yields physically acceptable results, with a smaller bounce as compared to the original CdL. Here we also show that a regular instanton as well as its neck features can be obtained without having to resort to the method of potential reconstruction discussed previously in the literature. Finally, we also discuss tunneling from de Sitter to Minkowski as well as to anti-de Sitter.