Abstract: A drilling fluid to be circulated through a borehole as it is drilled is produced by mixing solid and liquid drilling fluid components in such proportions that the density of the fluid has a selected value which lies between upper and lower limits (c) calculated for all depths of the borehole to be drilled. The lower limits satisfy a shear failure criterion for the material forming the wall of the borehole and above which influx of pore fluid does not occur, and the upper limits satisfy either the same shear failure criterion or a tensile failure criterion, depending on which of the two criteria predicts the lower upper limit. Upper and lower shear failure values (b) are calculated as a function of depth and tensile failure values (a) are calculated as a function of depth. The calculations include determining the in-situ stress state at the site of the borehole, and calculating the stresses which will occur at the borehole wall as a function of depth and drilling fluid density.