The paper relates the magnitude of the error bounds of data, used as inputs to a Gaussian dispersion model, to the magnitude of the error bounds of the model output. The research addresses the uncertainty in estimating the maximum concentrations from elevated buoyant sources during unstable atmospheric conditions, as these are most often of practical concern in regulatory decision making. The ability to develop specific error bounds, tailored to the modeling situation, allows more informed application of the model estimates to the air quality issues. The numerical uncertainty analysis is performed using the Monte Carlo technique to propagate the uncertainties associated with the model input. Uncertainties were assumed to exist in four model input parameters: (1) wind speed; (2) standard deviation of lateral wind direction fluctuations; (3) standard deviation of vertical wind direction fluctuations; and (4) plume rise. The authors conclude that the error bounds for the estimated maximum concentration and the distance to the maximum can be double that of the error bounds for individual model input parameters. These results allow estimation of minimum bounds on errors in model output when considering reasonable input error bounds.