Neural network analysis was used to construct models of unconfined compressive strength (UCS) as a function of mix composition using existing data from literature studies of Portland cement containing real industrial wastes. The models were able to represent the known non-linear dependency of UCS on curing time and water content, and generalised from the literature data to find relationships between UCS and quantities of five waste types. Substantial decreases in UCS were caused by all wastes; except for EAF dust, the effect was nonlinear with the greatest decrease caused initially by approx. 12% plating sludge, 40% foundry dust, 58% other ash, and 72% MSWI fly ash by mass of dry product. It appears that the maximum waste additions used in modelling may approximate the practical limits of waste additions used in modelling may approximate the practical limits of waste addition to Portland cement, i.e., 50% plating sludge or EAF dust, 64% foundry dust, 92% other ash, and 85% MSWI fly ash by mass of dry product. The laboratory was found to be a key predictive variable and acted as a surrogate for laboratory-specific variables related to cement composition, strength and hardening class, product mixing and preparation details, laboratory conditions, and testing details. While the neural network modelling approach has been shown to be feasible, development of better models would require larger data sets with more complete information regarding laboratory-specific variables and waste composition.