Filling apparatus (10) and method for automatically filling containers (100) for smoking articles with an incoherent material (M) of a smokable type. The apparatus (10) comprises delivery devices (22) comprising metering means (40, 41) configured to deliver a determinate quantity of incoherent material in each container (100). Each delivery device (22) comprises a funnel-shaped conveying member (52) which is configured to be made to vibrate during the delivery of the incoherent material (M) so as to prevent the incoherent material (M) which has been delivered by said metering means (40, 41) from accidentally remaining inside the conveying member (52).