Abstract: Viscoelasticity, compressibility and the pressure wave transmission of the gelled crude oil are significant influential factors during the pipeline restart process. This paper classifies the viscoelastic-thixotropic models of the gelled crude oil during the structure breakdown, and analyses the influential factors on the pressure wave transmission during restart process. The paper makes an introduction of the mathematic models of the gelled oil restart and emphasizes on the new models in recent years, including CNR & DNCR restart models and Vinay G, Negr ã o restart models. The key to the pipeline restart is the accurate determination of the compressibility of the gelled oil and wave transmission during the restart process, which will lay a foundation for further study of the restart of the gelled oil pipeline.