This article is devoted to thermal vibration convection studying in the non-Newtonian liquid type. In this work these equations of average liquid flow were obtained for Williamson's model and Ostwald — de Will's model. Quasy-equilibrium condition for non-Newtonian liquid in an arbitrary shape hollow was formulated. On the base of rheological Williamson's model a problem of vibration convection flow of nonlinear-viscous liquid in flat infinite vertical layer was considered.