The paper presents a stochastic method to test the soundness of accounting based solvency of banks, over a five-year period, and to define a proper capital adequacy level inductively, from a very limited subset of balance sheet indicators. A review of the literature about stress testing and capital adequacy is provided first, aimed to give evidence of the existing approaches in use and their critical aspects. Then, starting from a sample of 246 listed banks, a few balance sheet indicators are considered. Having set a critical threshold for each of them, according to the regulatory prescriptions, their effective values are forced according to different confidence levels, and two separate kinds of vulnerabilities are defined for the individual banks. These values allow to build a “bank Resilience index” (bRi), which is a measure of the capability to stay within the threshold limits (in other words, to remain solvent). We conclude that the approach could constitute a new, powerful alternative to test “financial soundness”, inasmuch it can give evidence of which banks are solvent, actually, as a consequence of a temporarily efficient mix of ratios, and which banks show a higher resilience for being truly much stronger. In effect, the bRi candidates itself to be a major health check indicator, suitable for surveillance purposes.