IF we are talking about EMT gear, there are specialized packs for that. Try googling for search and rescue suppliers - expensive but built to protect the gear from being tossed in and out of jeeps, with specialized compartments and durable materials.

If we are talking about just a layperson with first aid training who's toting a few SAM splints and a sizable kit in addition to his own gear, look at extended day packs in the 30-40 liter range. Gregory has some that can carry up to 40 lbs - I have my SAR gear in one, and have also used it for multi-day backpacking with a bear canister.