It depends very much on the situation/context.

rare: Don't feel you have to be polite = say what you mean without restriction.
Don't feel inhibited = This is a more casual affair than you thought it was.
Feel free!, usually as an answer to a question.
Don't force yourself! entails an ironic pre-conception of what the other person desires.

In all those contexts you could use "tu dir keinen Zwang an", and the "Zwang" can be a real or a supposed restriction or force, but whenever you use it it is a casual remark intended to disperse feelings of uneasiness or to create a less formal atmosphere. It is therefore rarely used with the "Sie"-form: "Tun Sie sich keinen Zwang an" could IMO only be used by persons who know each other well even if they are on the "Sie"-basis, e.g. employees in a firm, police officers, teachers outside of classrooms talking to each other etc., who see each other every day.
In more formal context, the effects shown in the examples above would be achieved by using quite different expressions.

Exhaustive enough? Feel free to say "no".

@sammy: No, I think this is the opposite direction. You say "don't feel like you have to" not when you feel that the other person is under some pressure, but if you have exerted the pressure yourself. You make a suggestion, the other person hesitates, you notice and try to alleviate the pressure: "Du musst aber nicht", "Nicht, dass du müsstest", "Du kannst natürlich auch anders", depending on context. If you said "Tu dir keinen Zwang an" in such a situation, you would increase the pressure.
Example: You go out with someone you barely know and say something like "What would you think of a cup of coffee in my place?" If you add "Don't feel like you have to", you create (or pretend to create) a loophole for the other person. If you said "Tu dir keinen Zwang an!", you are extremely pushy, implying something like "I know very well what you are up to, so come on, admit to it!"
This is a typical "language lab" discussion, but maybe the request by JadeMoogle US (what a name!) was for a proper translation. In which case, I'm afraid, context is compulsory (to stay with "Zwang" here!).

@sebastianW: "don't feel lie yu have to" means exactly the same as "tu dir keinen Zwang an" in certain situations. It is meant to be sarcastic, much like the German phrase is.

"don't feel like you have to..." sorry 'bout the typos. :-)

Hello? Probably it's just the stress of shopping and wrapping and mailing and cooking and decorating that made everyone here forget to check the three previous threads in the archive?

Suche in allen Foren: keinen+zwang

Still, just because it's the season of peace and goodwill, I have done my good deed for the day and put this (hastily) in New Entry.

related discussion: Feel free - Tu dir keinen Zwang an

If anyone else feels a surge of holiday spirit and could bear to post a comment there, that would be just peachy. (-:

Thanks very much to all for the helpful responses. @hm: I'll be more careful next time -- now, back to wrapping presents. :-)

Don't feel obligated to show up at the party.

Suche: obligated