Father of medicine's pachyderm cases (11)
I believe the answer is:
hippocrates
'father of medicine's' is the definition.
(I've seen this in another clue)
'pachyderm cases' is the wordplay.
'pachyderm' becomes 'hippo' (I've seen this before).
'cases' becomes 'crates' (crating is a kind of casing).
'hippo'+'crates'='HIPPOCRATES'
(Other definitions for hippocrates that I've seen before include "He offered oath" , "celebrated doctor" , "he produced an oath" , "Greek physician" .)