First, try and define the reason. For example, is it that they're shy, or is it that you're asking them to read something that is too difficult for them? If the first, you need to get them to be a bit less inhibited. Some ideas :
a) Play follow my leader reading. Use a simple dialogue with short phrases. You read out the first and they repeat. You then whisper the next and they must whisper it too. You shout the next, and they follow suit - and so on. Whatever volume you use, they must follow. Do it chorally first with the whole class to give confidence, then with half the class, then smaller groups, and finally individuals. You can do the same adding emotions too - saying it happily, sadly, angrily etc.
b)Similarly, practice very simple phrases being said in a way that expresses different emotions. For example, take the phrase
What's the time? and get them to say it as if a) they're very,very late for a flight b) they're in a very long and boring lesson c) It's five seconds before midnight on New Year's Eve and they're waiting to crack the champagne - and so on. You can do some of these at class level using choral and individual repetition. Then once they've got the idea, choose a different phrase but turn it into a game : give individual students the situation written on a flashcard. They have to say the phrase in that way, with movement and gestures if necessary, and the other students have to guess how the speaker is feeling and what the situation is.
c) Get them to read round the class using a text with very simple, fairly short sentences- one sentence per person. Start off the reading with music playing very quietly in the background, but after each sentence turn it up slightly. Tell them in advance what you're going to do and that you they must always speak loud enough for you to hear them. If you can't, put your hands to your ears and yell "Can't hear you!"
These activities must be fun and non-threatening for the students or they'll be counterproductive. That's why it's important to use simple texts - they shouldn't have to worry about the language while they're doing it. There should be a lot of laughter.
if, on the other hand, the problem is that they're daunted by the texts themselves, think about these principles :
a. Texts for reading aloud should always be slightly below students actual comprehension ability.
b. The text should always be read silently, and comprehension fully checked before students are asked to read aloud.
c. reading aloud is not a natural activity - it's a skill which needs to be taught actively. For some suggestions on how see an article which I wrote for my site
here.