A version of a network model of quantum Hall systems is studied classically. We assume that randomness inherent in the problem enters the model via random heights of saddle points only. We use ideas from classical percolation theory to calculate numerically the fractal dimension df, the correlation length exponent ν, the diffusion coefficient D, the corresponding exponent k, and other parameters of interest. The width of the longitudinal conductivity peak scales with the classical localization length exponent ν. © 1996 The American Physical Society.