A series of undrained monotonic triaxial compression tests were performed on natural, medium-dense (relative density (RD) = 50%) Chlef sand containing 0.5% of non-plastic fines, under different confining pressures of 50 kPa, 100 kPa, and 200 kPa. This article focuses on distinctive states of the monotonic undrained response of sands, namely the critical state, the phase transformation state, the quasi-steady state, and the state of undrained instability (onset of flow liquefaction). Specimens were prepared using dry funnel pluviation and wet deposition to investigate the effect of the initial sand fabric on these states. The present data suggest that the initial fabric of the sand appears to have a significant effect on the undrained behavior in the early stages of shearing, with its influence vanishing at large strains. Wet deposition specimens demonstrate considerably larger undrained instability state strength than their dry funnel pluviation counterparts, and a unique critical state locus is reached by both dry funnel pluviation and wet deposition.