Biodegradable and resorbable polymer pouches are described for use with cardiac rhythm management devices (CRMs) and other implantable medical devices (IMDs), i.e., a pouch, covering, or other receptacle capable of encasing, surrounding and/or holding the CRM or other IMD for the purpose of securing it in position, inhibiting or reducing bacterial growth, providing pain relief and/or inhibiting scarring or fibrosis on or around the CRM or other IMD. Optionally, the biodegradable and resorbable pouches of the invention include one or more drugs in the polymer matrix to provide prophylactic effects and alleviate side effects or complications associated with the surgery or implantation of the CRM or other IMD.