I've just tried out the example shown in the docs page but I always get this error when trying to use prompt.
I've also inspected $mdDialog and it returns:
Object {}
alert: (arg)
build: (arg)
cancel: cancel(reason, options)
confirm: (arg)
destroy: destroyInterimElement(opts)
hide: hide(reason, options)
show: showInterimElement(opts)
__proto__: Object
Nevertheless I've checked that prompt is listed as a preset in the source code, but I didn't go any further to figure out why it's not being added.
+1 Running into the same issue. Using material version 1.06
@soohoowoohoo The prompt is only available in v1.1.0rc1.
Everything works well in my demo.
http://codepen.io/DevVersion/pen/aNZXoY
@DevVersion it worked here, but since its on the master doc, shouldn't there be a note somewhere telling that we must use v1.1.0rc1 instead?
The docs (https://material.angularjs.org/latest/) clear say, which feature is included in which version.

Also the changelog is saying, that the prompt, is only available in v1.1.0rc1
https://github.com/angular/material/blob/master/CHANGELOG.md
I'll close that issue, because everything works as expected. If you have any further questions, just let me know ;)
Most helpful comment
@soohoowoohoo The prompt is only available in
v1.1.0rc1.Everything works well in my demo.
http://codepen.io/DevVersion/pen/aNZXoY