For the Presocratics, soma is, for one thing, that which occupies space; typically also, the elements (stoicheia: earth, air, fire, water) or the atoms (atoma) of Leucippus and Democritus are thought of as somata.
For human beings one finds an analysis into body and soul, soma and psyche. In the Cratylus (400b-c), Socrates suggests that some people thought that the soma is the sema of the soul, an ambiguous word that can mean either “tomb” or “sign.” He goes on to attribute to the Orphics a derivation of soma from the verb sozetai, kept or saved, in that the soul is “kept” in the body until “the penalty is paid.”
In the Timaeus, Plato derives the classical elemental “bodies” from triangles formed into regular solids (53ff), In general, however, he is more interested in human bodies, and their relationship to souls. In the Phaedo, for example, Socrates, about to die, assures his friends and associates that he will be well rid of his body, that the body is a kind of prison that distracts the mind. In the latter part of the Timaeus, for example, a more complex relationship of soul and body is presented, arguing that many “mental” illnesses can be attributed to bodily conditions (86bff).
In the Sophist, at 246ff, the Eleatic Stranger discusses with Theaetetus the history of theories about body in a passage called the Battle of the Gods and Giants: the Giants are those who believe that only bodily things are real, while the Gods believe in incorporeal forms and souls.
Aristotle has a great deal to say about all the senses of soma, from the mathematical sense (three-dimensional object, Metaph. V.13), to the basic physical sense (you cannot have two bodies in the same place at the same time, GC 1.8, 321a8), to the body of astronomical entities (Cael. 1.3) and the four terrestrial elements, to the bodies of living animals. One might well say that Aristotle’s philosophy is focused on bodily existence, not reductively, but in all aspects of the capacities of bodily entities to function in their environments. See also ASOMATON. (HDAGP)