What can be done to correct a problem of leakage after heavy rain? It accumulates on the floor in the rear.

Depending on the year, it could be the rear window reveal seal leaking or rear deck lid area leaking. :?

Welcome to the forum! If you put your year and model in your signature (from your profile) it'll help alot with diagnosis of some problems.

Do you have the stock sunroof? If so, your pillar drains may be plugged.

Yeah, if you have the sunroof your hoses that drain from it could have plugged and disconnected. I had the same problem in the rear floor and under the back seat. Took forever to find the root of the problem but just pulled back part of the ceiling and found they were disconnected, and stuck 'em back together.
Hope you have a sunroof cause this may be easy for you to fix, after you get up all the water

Thanks for the suggestions. Our 1995 Bonneville SSEi does have a factory installed sunroof; will check the hoses out.

And you may need to check under the backseat. Feel around, it may be soaked from water. I had to take my seat out it was so drenched. You may notice if your hoses are to blame that the corner of the ceiling above the rear door will be soaked with water. That'* how I figured it was my hoses. Good luck.