In a new approach used to model quench tests conducted with long cylindrical specimens in fluids, heat transfer within the fluid is described by the heat conduction equations while heat convection is neglected. Analytical solutions for the temperatures and stresses as functions of the time and of the radial coordinate in the cylindrical specimen are presented and the maximum tensile stresses in the specimen are shown to depend on the ratio of thermal conductivities and on the ratio of volumetric heat capacities in the specimens and the quench bath. Plots of maximum tensile stresses are given for a wide range of these ratios and plots of temperatures, stresses and heat fluxes are included for five conductivity ratios. It was found that the maximum stresses predicted by this analysis are in satisfactory agreement with experimental results in the literature for high conductivity fluids, while a larger discrepancy was noted for low conductivity fluids. / M.S.