Posting peer reviewed but not yet accepted papers to arXiv Here  Elsevier say that authors may put preprints on arXiv, and that they may put accepted versions on arXiv. They define a preprint as something that has not been peer reviewed, nor had any other value added to it by the  publisher. 

They do not seem to say anything explicitly about posting intermediate versions, that is, versions that have been revised as part of the peer review process but have not yet been accepted. 

I would like to post to arXiv a significantly revised version of a paper that has been accepted subject to minor revisions. The Elsevier website does not seem to address this case. Is posting the paper acceptable? Is it common practice?

The rationale for wishing to post this version is to be able to refer to new results it contains. But I can understand a journal not wanting such intermediate versions to be posted. Their peer review process has added value, but until the paper is accepted it's hard to give the journal credit.
I'm not a lawyer, but their definition of "preprint" says:


  This is the author's own write-up of research results and analysis that has not been peer reviewed, nor had any other value added to it by a publisher (such as formatting, copy-editing, technical enhancements, and the like).


Note all of these - formatting, copy-editing, technical enhancements - are done by the publisher's staff. Peer review is not usually done by the publisher's staff. So I'd say you are clear to post revised-but-not-yet-accepted papers to arXiv.

In any case the worst case scenario is probably them sending you a warning asking you to take down the revision (I consider this rather unlikely too - even if it's against their policies, they would first have to notice, and then have to decide to enforce). So you can probably do it without incurring too much trouble. If you're very worried, you can also ask them.