From the FAA site, subject to the whims of anyone that feels like it:
Each traveler will be limited to one carry-on bag and one personal bag (i.e., purse or briefcase).

I have been carrying a soft sided briefcase with my computer, cables, papers, etc, etc, (way to much etc) for about 8 years now. I do not carry a computer bag for a few reasons, they are too heavy and bulky and you can not put all your stuff in them. Hence, the multipurpose briefcase.

Anyways, I ramble. On both flights today, no problem. It is my briefcase and it fits under the seat in front of me.