The fountain flow of a non-Newtonian fluid during a circular pipe filling is investigated. Mathematical description of the process is based on the equations of motion and continuity. The system of equations is completed by the Ostwald-de Waele rheological equation. The slip condition is used at the contact line. The numerical solution of the formulated problem is obtained using a computational technology based on the finite volume method, SIMPLE procedure, and invariant method, which is used for numerical realization of the boundary conditions on the free surface. The results of parametric studies of the flow kinematic characteristics are presented depending on the governing dimensionless criteria and power-law index. (c) 2018 American Institute of Chemical Engineers AIChE J, 65: 850-858, 2019