The Heimlich maneuver, as I was taught in CPR under the Red Cross, should NOT break or even really touch ribs. You have ONE chance, usually, and you just can't get enough force by pressing on ribs - this will just let a tiny amount of the air you need escape around the edges of the blockage. You position your hands (or fingers in the case of an infant or small critter like a bunny) BELOW the ribcage and push as hard as you can upward and inward, into the rib cage, NOT pressing on the ribs themselves. This forces the tissues of the intestines up into the chest cavity, forcing the lung cavity to take up less space, which forces air into the blocked windpipe. Expect massive internal bruising, but not broken ribs. DO NOT do this unless you are absolutely certain that the windpipe is completely sealed. You need the pressure of a seal to do anything - that pressure is what pops the offending object out.

Suzi
Bunny Caregiver
Trained in CPR and the Heimlich maneuver by American Red Cross


More information on the Heimlich maneuver:

Heimlich Institute
Heimlich Maneuver for Pets