Erosional creep of grains attributable to the gradient of fluid pressu
re is considered. Drag forces arising from viscous fluid flux may disl
odge grains from the skeleton and initiate solid flux, which can lead
to systematic erosional creep of granular fabric as a whole. The proba
bility of local jumps of grains is stipulated by kinematic and local y
ield conditions that must be met at the same time. Average grain veloc
ity is obtained as a function of the local fluid pressure gradient. En
hancement of fluid flux attributable to simultaneous granular creep is
also estimated. The rate of erosional creep is calculated both for th
e water- and the heavy-oil-saturated granular fabric. Slow and moderat
e movements of silty slopes can be explained by the erosional creep ca
used by water flow. Flow of heavy oil can cause erosional creeps of sa
nd fabric with the rates of the same order of magnitude as the heavy o
il ones.