A machine for making and packing capsules (2) for extraction products in multi-capsule packs (27) includes a feeding station (11) for feeding rigid bodies (3) of the capsules, a dosing station (12) for dosing a dose of product within the rigid bodies, a closing station (13) for closing an upper aperture of the rigid bodies with a respective lid (7); a transport element (8) that features a plurality of seats (10) for housing and moving the capsules through the stations; an exit station (17) adapted to draw the capsules from the transport element; and a packing station (23) adapted to pack the capsules in multi-capsule packs where the capsules are arranged side by side and according to a head-to-tail orientation. The invention further provides for a method for making and packing capsules for extraction products in multi-capsule packs.