Several rabbi's have told me that one is prohibited from using an umbrella on Shabbat because one is "constructing a shelter".
Assuming they've used the correct reasoning, I'm not following it. I understand a "shelter" to be like an enclosed area that protects one from outside elements. More like a structure. A shack or a tent would protect you from rain. An umbrella only protects the top of your head, until the wind blows it. You still get wet on the sides.
Conversely, if you were to say, well, it is a "shelter" because at least it protects some part of you from the rain, then why not prohibit a hat or a good which also protects you?
Perhaps, the reasoning wasn't explained to me completely.