Aims. Within a 400pc sphere around the Sun, we search for Praesepe's tidal tails in the Gaia Data Release 2 (DR2) data set. Methods. We used a modified convergent-point method to find stars with space velocities close to the space velocity of the Praesepe cluster. Results. We find a clear indication for the existence of Praesepe's tidal tails, both extending up to 165pc from the centre of the cluster. A total of 1393 stars populate the cluster and its tails, giving a total mass of 794M☉. We determined a tidal radius of 10.77pc for the cluster and a tidal mass of 483M☉. The corresponding half-mass radius is 4.8pc. We also found a clear indication for mass segregation in the cluster. The tidal tails outside 2 tidal radii are populated by 389 stars. The total contamination of our sample by field stars lies between 50 and 100 stars or 3.6-7.2%. We used an astrometrically and photometrically clean subsample of Gaia DR2, which makes our Praesepe sample incomplete beyond MG~=12.0mag; this corresponds to about 0.25M☉. A comparison with an N-body model of the cluster and its tails shows remarkably good coincidence. Three new white dwarfs are found in the tails.