An HR rep came from Exponent (along with some associates) to give a presentation to our department in my university. I talked to the HR rep afterwards, we exchanged emails and set up a phone interview. The phone interview was straight forward, they are just trying to see if you are a good fit to be a consultant. Because of my background, they sent me out to the Menlo Park office for an on-site interview.
The on-site interview lasted the day (early morning to ~ 4pm). Started with an interview with HR, discussed comp etc. Then I gave a seminar on my research, the questions were fairly easy since they were not experts in the work I do. Then I had a number of meetings with various associates. Some higher level managers gave me questions on past projects and asked me to think of a way to come up with a solution. At times, this was challenging but they gave hints. It really wasn't that difficult though if you can think a problem through and also think on your feet. A lot of associates asked why I wanted to be a consultant. Fairly easy to BS that answer, just tell them you are done with research and looking for ways to apply your background to areas outside of academia. Also, tell them you are interested in high-pace projects, multi-tasking, working with a lot of people, etc. Interview ended, I got an offer in the mail within a few days.