The complex phenomenon of suffusion is the selective erosion of the fine fraction under the effect of seepage flow within the matrix of coarser particles. Three processes are involved simultaneously: detachment, transport, and partial filtration of the fine particles. With the objective to characterize the influence of the stress state on suffusion-related parameters, downward seepage flow tests were conducted under hydraulic-gradient controlled conditions. Four stress states are investigated: triaxial isotropic, triaxial compression, triaxial extension and rigid vertical boundaries. Also, four different cohesionless gap-graded soils were tested, from underfilled to overfilled microstructures. The entire erosion process can be divided into four phases: onset, self-filtration, blow-out and steady state. The definitions of several suffusion-related parameters are given for each suffusion phase, in terms of hydraulic gradient, hydraulic conductivity variation, cumulative expended energy, erosion resistance index and Darcy velocity. The results demonstrate that the suffusion kinetics of soils in transition between underfilled and overfilled microstructures are more affected by the stress state than others.