A model that can approximately describe a non‐Newtonian fluid such as paint and fluid mud is a Bingham plastic with a yield stress. To facilitate the study of slow but transient spreading of a thin sheet of fluid mud, we need the approximate equations governing the nonlinear motion. Beginning with a modified Bingham model with two viscosities, the approximate equations are derived by a systematic perturbation analysis. The controlling parameters are found to be the Reynolds numberR, the shallowness ratioh¯/L¯=&dgr;1/2, and the ratio of viscosities &bgr;=&ngr;/&ngr;1[as defined in (45)]. Results valid forR,&bgr;,&dgr;≪1 but &dgr;/&bgr;2≤O(1) are obtained. In the special case when &dgr;/&bgr;2≪1, the limits can also be obtained by heuristic arguments similar to those in the lubrication theory. Two examples are discussed.