Many aspiring actors have written to be saying that they have trouble expressing emotion on stage. They feel the emotion, but they just cannot get it to come out.
Acting involves giving free and open expression of ones emotions. But many would-be actors are inhibiting themselves by worrying about what others may think of what they are doing (crying or screaming or whatever) and they are worrying about how they may look doing those things. The actor's mindset must be that she doesn't care what people think; and furthermore she enjoys the opportunity to have free expression of her emotions. That is one of the joys of acting--society makes us suppress our emotions but acting allows us to express them fully which is a refreshing and enjoyable experience.
To be an effective actor, the actor has to get out of her head. She gas to stop thinking about what she is doing and what others may think of it. Acting is not thinking, it is emotionally responding. Acting requires that the actor's entire being (all of her senses) focuses on the scene, and does not allow her mind to wander into thinking about other things. Concentration is one of the basic requirements for the actor.
Aspiring actors can practice emotional expression without inhibition in acting classes or with a good acting coach. And they can read about how such expression works and how it is the basis of acting in such books as How to Stop Acting by Harold Guskin and The Tao of Acting by Kenneth Plonkey.
On my website there are several articles that may help actors with emotional expression as well: "Modern Times Need Modern Methods", "Tao and The Art of Acting", and "Truthful Acting". When you go to my web page at http://tao-of-acting.org you will find these articles under the Acting Theory button on the drop down list.
Finally to address one other problem: acting is not leaving yourself. In order to be effective the actor allows her emotions to be expressed. Actors do have get out of their heads: they need to stop thinking about what they are doing and just do it and not think about anything but the scene. Actors have to learn to like who they are and how they look and to heck with the rest of the world (as long as they are getting parts). It is not necessary to be a beauty queen to be an actor. It is necessary to be able to act without inhibitions. Experience on stage should help a great deal. Go to my website, read my book and the articles and ask me lots of questions. God bless, Doc