From Mark Griffith, Sophocles: Antigone (Cambridge, 1999), pp. 37-38.

Distinctively drawn through each of these figures is, we should acknowledge none the less that their internal psychological states and personalities, i.e. their true "characters" as such that behind their dramatic masks, remain largely unformulated by the text, and thus beyond our consideration.^NOTE  Rather, we may say that Ant. and Kreon embody and articulate the most typical and generalized characteristics of their precisely defined social roles - Ant. as the devoted sister and unmarried daughter, Kreon as the stern soldier-ruler and father, each of them fiercely determined to resist any threat to the integrity of these roles.  This is not to say they are not convincing, even memorable, dramatic "characters"; rather, that we are not encouraged by the text to ponder the inner workings of their minds.  The meaning of the play lies for the most part elsewhere.

NOTE:
The text does raise some interesting possibilities, however, about which we are at liberty to speculate:  are Ant.'s (or Ismene's) personality and motivations shaped by (consciousness of) incestuous origin Ö ?  Or by resentment of her uncle's new authority?  What do the Chorus really feel about Ant. and Haimon, and about their king?  What are Ant.'s feelings for Haimon?  What goes through Kreon's head when he encounters Haimon at the tomb (1226-30)? etc.  Out of such questions Ö we may construct our own new dramas.
 
 

From: A. M. Dale, Euripides: Alcestis (Oxford: Clarendon Press, 1961), pp. xxiv-xxv; xxvii-xviii.

The root of the trouble [i.e., psychological interpretation of Admetus and Alcestis] is, I think, our inveterate modern habit of regarding a drama almost exclusively in terms of its characters. The modern conception of the actor's function, with each actor concentrating on the 'interpretation' of his single part, strongly reinforces this habit.  It works quite well with modern drama ... But it will not work satisfactorily with Greek tragedy. Of course the Greek, like every serious drama, involved 'character', whose part in the action, and therefore whose words, to some extent reflect their several natures.  But in Greek tragedy their speeches, and the interplay of their dialogue, can rarely be interpreted as primarily or consistently expressive of their natures, and whenever we find ourselves trying to build up some elaborate or many-sided personality by adding up small touches gleaned from all parts of the play we can be pretty sure of being on the wrong lines.  It usually means that we are not allowing enough for two considerations always very important to Greek dramatists, the trend of the action and the rhetoric of the situation.
... [Section on trend of the action was omitted.]
Admetus as a person is blown hither and thither by every wind of incident; he is a person to whom things happen, it is his experience that matters, his reactions to what people do or say to him ... .  So far from considering the Alcestis a full-length study of naïveté, weakness, hysteria, egotism, character-development, and so forth, I do not believe that ... Euripides had any particular interest in the sort of person Admetus was.  The situations in which the plot involves him are too diverse for much personality to appear, or to be intended.  For in a well-constructed Euripidean tragedy what controls a succession of situations is not a firmly conceived unity of character but the shape of the whole action, and what determines the development and finesse of each situation is not a desire to paint in the details of a portrait-study but the rhetoric of the situation ... .  Rhetoric is a concept which we tend to hold in some suspicion, as if in its nature there must be something slightly bogus; but we shall never properly understand Greek tragedy unless we realize how closely related were the rhetoric of Athenian life, in the assembly and law-courts and on other public occasions, and the rhetoric of the speeches in drama.  Nourished on the psychological novel, we tend to assume that the poet had brooded on the story until the characters took shape in his mind, as if he had asked himself: What would X, being such a man, be likely to say in such a situation? Whereas we might sometimes get nearer to the meaning by imagining the question: suppose a man involved in such a situation, how should he best acquit himself? How gain his point? Move his hearers? Prove his thesis? Convey information lucidly and vividly?