The evolution of stresses and strains in a zirconia-containing refractory tube subjected to a hot shock on the outer surface and convective cooling at the inner surface is analysed with the method of finite elements. To account for the temperature-induced phase transformation in the zirconia as well as the overall thermal expansion, a coefficient of total dilatation is introduced. The parameters that control the time-dependent stress and strain responses are identified by performing finite element calculations that span the range of variables relevant to steel making. The effects of tube thickness, hot shock duration, initial temperature, temperature dependence of elastic modulus, and transformation amplitude on stress and strain distributions are discussed, and heating and process strategies to eliminate surface cracking are suggested.