The Lagrangian particle dispersion model, FLEXPART, which includes additional parametrizations for transport by subgrid-scale convection and turbulent eddies, is employed to investigate stratosphere-troposphere exchange (STE), based on 15 years of ECMWF global atmospheric reanalysis data (ERA-15). The model was initialized with 500,000 particles, distributed randomly throughout the atmosphere, and these were subsequently advected continually over the reanalysis period. The methodology employed in FLEXPART, allowing various age properties and pathways of air masses to be traced permanently on a very wide range of timescales, is described in detail. Empirical validation of the model results is presented. It is shown that typically more than 95% of the mass of the troposphere at any one time has been in the stratosphere within the preceding year, emphasizing the significance of STE. Cross-tropopause fluxes reveal regions of mean downward net flux in the subtropics flanked by mean upward net flux in the tropics and, more weakly, in the polar regions. Estimates of the mean net downward cross-tropopause flux in the northern extratropics agree well with other studies but are shown to be highly sensitive to the choice of latitude at which the extratropics are defined to begin. The mean age of tropospheric (stratospheric) air in the stratosphere (troposphere) is derived and shown to be somewhat underestimated, especially for tropospheric air at higher levels of the stratosphere, due largely to deficiencies in the vertical resolution of the ERA-15 stratosphere.