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A simple tool for evaluating the stability of the finite-element beam propagation method (FEBPM) for lossy waveguides is described. Current stability issues are explained by this method. The sufficient stability condition of the FEBPM is described. The stability of the analytical propagation function, the Crank-Nicolson propagation scheme, and various Padé approximants are analyzed using the tool. The dependence of the stability of the FEBPM on the propagation step size is also noted.