AbstractSimple axi‐symmetric uni‐axial compression tests have been realized on dry loose samples of glass beads (diameters d: d=0.2 ± 0.05 mm, 0.75 ± 0.1 mm, or 3 mm) and on Hostun sand under small lateral confinement, σ3<60 kPa, using different sample sizes. The experiments with the two smallest spheres (d=0.2 and 0.75 mm) exhibit stick‐slips, which are characterized by (i) a rapid release Δq of the deviatoric stress q and by (ii) the strain Δε1 separating two events. The samples which exhibit stick‐slip also present a weakening of strength q(ε1) as the rate of deformation dε1/dt is increased. No stick‐slip is generated during the first part of the q−ε1 curve, i.e. when q grows fast with ε1. Four different parameters helped us determine the statistics of Δq and Δε: the lateral pressure σ3′, the rate of deformation dε1/dt, the sample height H, and the diameter D. The statistics do not depend on rate history. They look like exponentials in small samples and/or in (large sample+fast dε1/dt), and they look like Poissonian or Gaussian in (Large sample+small dε1/dt). This change in statistics is attributed to a varying of triggering process starting from a single random event in small samples to multiple random events. We have interpreted this change of statistics as due to some finite size effect so that the representative elementary volume shall contain at least (200)3 grains. Localization of deformation is visible at the end of compression but cannot be detected from stick‐slip statistics nor from q vs ε curve. Copyright © 2004 John Wiley & Sons, Ltd.