Direct numerical simulation is utilized to generate statistics in particle-laden homogeneous plane strain turbulent flows. Assuming that the two-phase flow is dilute (one-way coupling), a variety of cases are considered to investigate the effects of the particle time constant. The carrier phase is incompressible and is treated in the Eulerian frame whereas the particles are tracked individually in a Lagrangian frame. For small particle Reynolds numbers, an analytical expression for the particle mean velocity is found, which is different from the fluid one, and the dispersed phase is shown to be homogeneous. This is not the case for particles with large Reynolds numbers and no statistics involving particle fluctuating velocity is presented for large particles. The results show that the root mean square (r.m.s.) of the particle velocity in the squeezed direction exceeds that of the fluid in the same direction and increases with the particle time constant. The mean velocity gradient component in the elongated direction has the opposite effect, that is the r.m.s. of the particle velocity is decreased below that of the fluid in this direction. Further, the dispersed phase exhibits a larger anisotropy than the fluid phase, and its anisotropy increases with the particle inertia. Dispersion is shown to depend strongly on the injection location and quantified dispersion results show that increasing the injection location coordinates in the strained directions increases the dispersion. (C) 2001 Elsevier Science Ltd. All rights reserved.