Matter-of-fact, Detached, Inquisitive, Hopeful
For the most part, the tone of Atlas Shrugged is straightforward and somewhat unemotional. It is often weirdly detached in places, which helps contribute to the book's vaguely mysterious, ominous atmosphere. We "hear" most of the novel through characters (Hank and Dagny especially) who coolly repress their emotions and approach situations with an almost clinical detachment. That isn't to say that deep emotion isn't lurking beneath the surface, but the book doesn't whack you in the face with angst and woe.
The book often employs the inquisitive tone of a newspaper article: it's curious and probing, like an investigative reporter. In the run-down of various disasters, the narrator often channels an inner journalist. The Taggart Tunnel collapse is a good example of this: the tone is detached and factual, wondering impersonally how something like that could happen and then shrugging when the disaster does happen. The tone of the book highlights deep emotions by not highlighting them. Instead of being melodramatic, the tone simply implies a lot of the emotions behind the scenes, leaving readers to fill in the emotional blanks.
But this isn't to say that the tone is always without emotion. It can be cautiously hopeful, even though that hope is often slightly diminished by a dose of harsh reality. Main characters are presented very affectionately, and the novel's philosophical ideals are treated optimistically. Even in the face of disaster, the narrative tone often hints at some hope for the future.