A visco-elastic-plastic mathematical model developed at Sheffield City Polytechnic was used to calculate the thermal stress and strain generated during the quenching of an infinite plate of high hardenability steel (835M30) in water, nine experimental oils and a polymer. In.the case of water, previous comparisons between experimental and calculated residual strains was poor. This discrepancy, during the present investigation, was reduced by introducing into the model the relationship between actual surface temperature and surface heat transfer coefficients and by incorporating the effects of various surface finishes into the model. However this discrepancy still remains to a limited extent. The same mathematical model was used to investigate the quenching characteristics of a number of experimental oils: overall the calculatedresidual stresses and strains compared well with the corresponding experimental data. The experimental oilscontained mixtures of additives. Those based on sodiumsulphonate increased the rate of cooling during quenching and the associated absolute residual stresses at a fixed point in the plate. Simultaneously the residual strains were reduced. The use of the succinimide additive produced converse effects in each case. The investigation also included the quenching of plates in polymer solutions of varying concentrations to provide a basis for comparison between the three most commonly used quenchants, viz. water, oil and water soluble polymers. The results indicated that in terms of the residual stresses and strains the oils produced smaller values particularly in the latter case when compared with the polymers. However when compared with water both the oils and water soluble polymers produced significantly smaller residual stresses and strains. The quenching characteristics were also investigated by the use of photography which gave an insight into the cooling characteristics of each quenchant. A water quench produced masses of fine bubbles during the nucleate boiling stage whilst this stage was characterised by large vapour blisters moving up the face of the plate in the case of the experimental oils. Previous photographic evidence indicated that solid polymer was deposited during quench and coated the plate with a gel-like substance which returned back into solution when the temperature was low enough.