Non-elemental (無属性, Muzokusei?, lit. No attribute) abilities and magic skills, such as Flare and Ultima, are those that do not have an elemental affiliation like Fire or Blizzard. Non-elemental abilities and magic skills cannot be absorbed by units who absorb elemental attacks.
The majority of Final Fantasy series attacks, including items, fall into the non-elemental category, and as such, cannot be reduced or nullified by simply equipping a piece of equipment such as Flame equipment or Tetra Elemental.
Instead, most non-elemental attacks must be dealt with either by using the Defend or Row commands, or the spell Protect, against physical attacks, while for magic non-elemental attacks, it can only usually be dealt with by utilizing the spell Shell.
Two recurring spells are Flare and Ultima, usable in almost every main Final Fantasy title, but Final Fantasy XIII. Comet, Comet 2, Meteor, and Ruin are also spells associated with this element. Gravity and Holy spells are often non-elemental in games which don't classify Gravity or Holy as elements.
Bahamut with his Megaflare is the most occurring summon associated with being non-elemental. Other summons affiliated with this element are Valefor with her Energy Ray and Energy Blast from Final Fantasy X, and Exodus with his Meteor from Final Fantasy XII.
Classical elements typically refer to ancient concepts similar to the modern states of matter: earth (solid), water (liquid), air (gas) and fire (plasma). Classical elements are the simplest form of existence, of everything in existence. Many philosophies and worldviews believe in classical elements.