Mudflows are natural, highly concentrated water-clay-grain mixtures that flow in mountain streams after long or intense rainy periods and may cause considerable damage if they overflow on the alluvial fan. The possibility of predicting the extent of these flows on the basis of material and flow parameters is examined. The simplest realistic case of a yield stress mudflow moving through a narrow open channel followed by a wide, long plane is considered. It is demonstrated that the unconfined flow of a yield stress fluid over an inclined plane cannot be uniform; even in steady state the flow width should increase continuously from the channel exit. A complete treatment of the flow equation on the basis of the long-wave approximation, including an appropriate three-dimensional expression for the constitutive equation, makes it possible to establish a system of equations from which flow characteristics at any point (longitudinal and lateral mean velocities and fluid depth) can be deduced. In particular, for a Herschel-Bulkley fluid with a flow index of 1/3 it is found that the lateral extent will increase proportionally to the distance from the channel exit to the power 9/20 and that, in the sheared part, the fluid depth in a cross section will have a parabolic distribution. Experiments have been carried out with fine mud suspensions (at different solid fractions) whose rheological behavior is similar to that of natural mudflows. The theory is in fair agreement with experimental data concerning fluid depth distribution but systematically overestimates lateral extent (by 30%). This is certainly due to the fact that the assumption of lateral extent much smaller than flow length is not respected in our tests. ¿ American Geophysical Union 1996