A new method to predict traveling bubble cavitation inception is devised. The crux of the method consists in combining the enhanced predictive capabilities of large-eddy-simulation (LES) for flow computation with a simple but carefully designed stability criterion for the cavitation nuclei. For LES a second-order accurate finite element model based on the Galerkin/least-squares method with Runge-Kutta time integration is applied. The incoming nucleus' spectrum is approximated by a Weibull distribution. Moreover, it is shown that under typical conditions the stability of the nuclei can be evaluated with an algebraic criterion emerging from the Rayleigh-Plesset equation. This criterion can be expressed as modified critical Thoma number and fits well into the LES approach. The method was applied to study cavitation inception in a flow past a square cylinder. A good agreement with experimental results was achieved. Furthermore, the principal advantage over statistical (time-averaged) methods could be clearly demonstrated, even though the spatial resolution and application of the LES were restricted by limited computational resources. As the latter keep on growing, a wider range of applications will become accessible methods for cavitation prediction based on algebraic stability criteria combined with LES. Copyrlght