A filament cassette and a filament loading assembly supply modeling filament to a liquifier in a three-dimensional deposition modeling machine. Two or more cassettes containing spooled filament are inserted into the machine. A strand of filament from a first one of the cassettes is fed to the liquifier for extrusion. Without operator intervention, the filament strand from the first cassette is withdrawn from the liquifier, and a filament strand from a second one of the cassettes is fed to the liquifier. The switching of filament feed sources is triggered by an event, such as an identification that the filament from the first cassette has reached a predetermined minimum length. In this manner, a used primary filament cassette is automatically replaced with a standby filament cassette, so that the machine need not experience downtime waiting for an operator to change the cassettes.