How to create an Observable from static data similar to http one in Angular?

Perhaps you could try to use the of method of the Observable class:

import { Observable } from 'rxjs/Observable';
import 'rxjs/add/observable/of';

public fetchModel(uuid: string = undefined): Observable<string> {
  if(!uuid) {
    return Observable.of(new TestModel()).map(o => JSON.stringify(o));
  }
  else {
    return this.http.get("http://localhost:8080/myapp/api/model/" + uuid)
            .map(res => res.text());
  }
}

As of July 2018 and the release of RxJS 6, the new way to get an Observable from a value is to import the of operator like so:

import { of } from 'rxjs';

and then create the observable from the value, like so:

of(someValue);

Note, that you used to have to do Observable.of(someValue) like in the currently accepted answer. There is a good article on the other RxJS 6 changes here.