To benefit the application of finite element method in industrial vessels, an advanced high temperature compressive creep device has been designed. This creep device possesses several advantageous characters. Relatively high mechanical loads up to 20 MPa can be applied. An uneven loading of the specimen is tactically avoided with a spherical piston and the loading concentration at the specimen surface is relieved through an intermediate compliant component. An accurate measurement of deformation is guaranteed through direct contact of corundum arms of extensometers with the cylindrical surface of the specimen. The onset of creep is well defined through recording the deformation while the loading procedure starts and applying a small pre-load on the specimen only during the preheating procedure. Associated with the developed creep testing approach, a general and robust inverse procedure using the Levenberg-Marquardt algorithm is developed to identify Norton-Bailey strain hardening creep law parameters. By fitting the strain/time curves the creep law parameters of refractories under various temperatures can be precisely and efficiently identified. The obtained creep results can be further used for the thermomechanical modeling activities. One of the consequences of creep of refractories during the process cycle is that the magnitude and distribution of stresses in the refractory lining are altered. In the case of a RH snorkel, the maximum compressive stress occurring during the thermal shock is not decreased significantly. With increasing process time, creep relieves the compressive stresses dramatically and even changes the stress direction. Besides, the occurrence of creep increases the risk of joint opening during the submerging. Cautions have to be paid when the Norton-Bailey creep model is applied. The application of time hardening/softening representations in industrial vessels with complex thermal and thermomechanical conditions will result in conclusions different to the case of strain hardening/softening law. Since strain hardening/softening representations display the better ability to reproduce the experimental results under various loading conditions, it is recommended to use strain hardening/softening representations for the thermomechanical modeling of industrial vessels. The classical creep model is hydrostatic pressure independent and may characterize the creep response of metals very well, but might overestimate the creep response of refractories under multiaxial stresses states. A Drucker-Prager creep model could be an alternative for this case, in which the creep is hydrostatic pressure dependent. The major impact of the Drucker-Prager creep model on the thermomechanical results of a RH snorkel is that lower creep strains and smaller joint distances are predicted.