The non‐Newtonian features of onset, saturation, and degradation exhibited by the flow of dilute water solution of linear polymers through a porous medium are described. A physical model for the non‐Newtonian behavior is presented as arising from the gradual extension of the polymer molecules, acting as elongated particles, and their alignment in the direction of flow. Comparisons are made with data from measurements in idealized porous‐media configurations.