Sigh... I complained long ago in WP talk pages that the articles on elasticity tended to be unreadable, disorganized, featured messy and uneven coverage of possible topics, and so on. The principle author took this well (the subject wasn't his thing, he was just trying to fill a gap in WP as best he could) and invited me to contribute improvements, but I never had time and eventually stopped editing the WP entirely (long story). I haven't had the heart to take a look to see if there has been any improvement.
Anyway, I'd advise that in general, WP should never be your only source for anything important, that you bear in mind that anyone can edit the WP (with all the consquences that implies for the instability and questionable reliability of this "encyclopedia"), and that you move on to real textbooks published by reputable publishers as quickly as possible.
Alas, in this particular area I don't know of any books which do a really
good job of explaining the fundamental ideas of the theory of elasticity in a reasonably brief space in a way suitable for contemporary students. Landau and Lifschitz, Theory of Elasticity, Vol. 7 in their Course of Theoretical Physics, Pergamon, 1986, might be your best choice, if you can find it. If your interest comes from physics rather than engineering, which seems not be the case here... If you read between the lines and can handle a somewhat idiosyncratic notation, Jeffreys and Jeffreys, Methods of Mathematical Physics, 3rd Ed., Cambridge University Press, 1972, offer a very brief overview. I'd be happy to hear recommendations from others! Gokul?