We present a simple and easy to implement statistical method of estimating masses of metal contaminants in a shallow industrial fill. The current metal concentrations are assumed to have resulted mostly from random mixing, crushing and placement of the fill. With this assumption, it can be shown that the metal concentrations should be lognormally distributed, i.e., the distributions of the concentration logarithms should be normal. The properties of the lognormal distribution are then used to calculate the expected masses of zinc, lead, barium, cadmium, copper, antimony and mercury in the soil. In addition, a neural network/statistical model is used to account for a possible spatial nonuniformity of metal concentrations. The neural network model predicts the total metal masses within a factor of two from the lognormal model. This means that a significant spatial nonuniformity exists in the fill, but more work is needed to validate the neural network model.