Wiktionary
midsole
n. The layer of a shoe in between the outsole and insole, typically there for shock absorption.
Usage examples of "midsole".
I was just reading a review in one of his running magazines of the latest in "Sport Utility Sneakers," as they are evidently called, and it was full of passages like this: "A dual density EVA midsole with air units fore and aft provides stability while a gel heel-insert absorbs shock, but the shoe makes a narrow footprint, a characteristic that typically suits only the biomechanically efficient runner.