Flows of mud, in the form of a large amount more or less natural fine particle (less than 100μm) suspended in water are often encountered in industry and nature (sewage sludge, submarine landslides, moutain mud-flows coal slurries, drilling muds, etc). Data concerning these flows are often empirical. We aim here to describe laminar, free suface flows of such materials. On the basis of the majority of rhelogial results concering concentrated mud suspensions the constitutive equation of such fluids can generally be assumed to follow a Herschel & Bulkley model. Consequently, in the case of uniform flow on an infinitely wide, inclined plane or in a semi-cylindrical channel, the velocity distribution within the fluid can be computed exactly. For uniform flow in open channels with other cross-section types we propose to detetmine the discharge eqution in the form of a relation between two characteristic non-dimensional parameters and aspect ratios. In the case of a gradully varying but steady flow on an infinitely wide, inclined plane we assume that shear at the wall, at a specific point, is identical to the value of the uniform flow for a comparable discharge and height. Using this hypothesis we demonstrate that the possible flow properties are quite similar to these met in usual free surface hydraulics (super-critical and subcritical regimes, hydraulic jump, roll waves, etc). We than present the results of uniform flows in an open channel with two types of cross-sections: rectangular and trapezoidal (α = 45°). The channel slope varies mainly in the range [2;40%], and the discharge is within the range [0.01;81/s]. The theory appears able to predict relatively well results concerning uniform flows along with roll wave open channel is vaild as long as the aspect ratio is less than 0.1. For each channel we propose empirical expressionas for the mean wall shear stress also valid for a higher aspect ratio.