An ostomy appliance is disclosed with an inflatable seal for sealing against the stoma. The inflatable seal has a first inflatable chamber portion for fitting inside the stoma to seal against the internal tissue. The inflatable seal also has a second inflatable chamber portion for sealing externally against the stoma and peristomal skin. In one embodiment, a tube extends through the inflatable seal to provide a communication passage for discharge of body waste without removing the inflatable seal. The tube floats with respect to an adhesive mounting member to allow a waist between the first and second inflatable chamber portions to self-locate in the stoma.