A mathematical solution is developed for the steady, quasi-static, plane strain advance of a shear fault in a fluid-infiltrated elastic porous material. As revealed through analysis of some elementary fracture mechanics models, the coupled deformation-diffusion effects in such a material lead to a required 'force' to drive the fault that increases continuously with fault velocity up to a maximum value. The nominal fault tip energy release rate required for spreading at this maximum is greater than that for very slow speeds by a factor approaching (1-&ngr;)2/(1-&ngr;μ)2, where &ngr; and &ngr;μ are the elastic Poisson's ratios under 'drained' and 'undrained' conditions, respectively. The effect is numerically significant and provides a mechanism by which a spreading shear fault can, within limits, be stabilized against catastrophic (seismic) propagation. Predictions of the model are compared to data representative of creep events on the San Andreas system. It is concluded that the speeds and slipping lengths of the observed events are consistent with their being stabilized by the effect discussed, and hence the model would seem to provide a viable mechanism for fault creep. Similar effects may be operative also in setting the time scale of progressive landslide failures in overconsolidated clay soils, in which rupture occurs by propagation of a narrow slip surface.