This paper discusses the undrained strength of heavily overconsolidated Izumi clay and a clay-sand mixed (C-S) soil at different states (i.e. intact, reconstituted, and compacted) in terms of the magnitude of strength and the degree of non-linearity of failure envelopes at low effective stress levels (5-20kPa), corresponding to the shallow slope failure expected at 1-2m of depth. A series of constant-volume direct shear (DS) tests supplemented by hollow cylinder (HC) simple shear tests was performed from low consolidation stresses. To express the non-linearity of failure envelopes at low stress ranges, a non-linear power law strength criterion was applied. The results suggest that the normalized strength and the degree of its non-linearity of Izumi clay at intact states were much higher than at equivalent reconstituted states, potentially due to true inter-particle cohesion. The compacted states led to slightly lower normalized strength than the reconstituted state in Izumi clay, while they did not result in significant difference in the C-S soil. Inclusion of coarser particle in a clayey soil seems to reduce the low stress level non-linearity of the strength envelopes at both states. All the above observations suggest that the low stress level strength characteristics and their dependence on states are significantly influenced by soil types; possibly by soil gradation.