A bonding apparatus and a bonding method are provided. The bonding apparatus bonds a semiconductor die to a substrate by thermocompression through an adhesive material. This bonding apparatus is provided with: a bonding tool which has a bonding surface that holds the semiconductor die through a first portion of a tape, and a pair of first tape constraining surfaces that are arranged so as to sandwich the bonding surface and constrain a second portion of the tape: tape constraining mechanisms which have a second tape constraining surface that presses the tape against the first tape constraining surfaces; and a control part which controls the movements of the bonding tool and the tape constraining mechanisms.