What would cause a thump and rattle in the undercarriage of a car

Check your suspension.. it may be something small , but, I would not want to chance it.

A broken muffler mount is a possibility.

Sway bar links/rods do that when bad, but a 2014. Does it have high miles?

Like everybody said before this It could be a many things, If its not something you can find on your own have a good shop mechanic look it over and/or drive it.

What were you doing just BEFORE you started hearing this?? Off road??

Could just be a shield, dust cover or inner fender plastic.

A carcass.

A Dead Body most likely !! Possibly a Bicycle also.

I had to replace the Suspension 2 times so far on my 2007 Jeep Compass !! 1st time at 40,000 miles !! Luckily I had Extended Warranty, TOTALLY DEFECTIVE SUSPENSION, SHOULD'VE BEEN A RECALL ON IT !!!

Steve - Happy New Year! You mean that the suspension on these supposed rugged vehicles are really not that robust?? Retorical question, LOL..... I have a 2010 Subaru Outback Limited with more than 80,000 miles, original suspension, shocks and struts, and I took it on some unmaintained roads in Sequoia Kings Canyon and Joshua Tree National Park with absolutely no PROBLEM. The problem is Chrysler products.

The ground clearance on the 2014 Jeep Compass Latitude is 8.2 inches, while the Subaru Outback is 8.7 inches, surprised????

In answer to the question from enginecreator, I do have high mileage , and the car has been hit 3 times, once on the front passenger side, and twice in the rear. I had the body work done and was not informed of any problems with chassis. I have replaced brakes, tire rods, etc.

Try to get it on a lift and have a tech drive it.

lainey81- what do you mean by "high mileage," for a 2014 model, are you talking about more than 60,000 miles??