My 2001 honda civic sounds really rough almost like a metal vibrating sound when I start the car and it is idleing, then the sound happens when I put it in reverse shortly after being started up. When the car is at an idle for a period the sound will sometimes happen also. When driving the car appears to be fine. Does anyone have any idea what could be causing this to happen? Please help!

How many miles on your Civic?
You may have failed motor/trans mounts.
Inspecting underneath is difficult due to low ground clearance, but it might be critical.
Another possibility is that the exhaust may have gotten bent and is contacting the underbody. Again, you need to take a look.
Either of these can occur when in reverse.
One way to check for failed mounts would be to open the hood and watch the engine while shifting through from say park to reverse, neutral to drive, etc. Set the park brake and hold your foot on the brake pedal. Watch for excessive engine movement, especially while applying some light throttle briefly while FIRMLY holding the brake pedal. Please, be careful. Don't let the car lurch forward or backward.

How many miles on your Civic?
You may have failed motor/trans mounts.
Inspecting underneath is difficult due to low ground clearance, but it might be critical.
Another possiblility is that the exhaust may have gotten bent and is contacting the underbody. Again, you need to take a look.
Either of these can occur when in reverse.
One way to check for failed mounts would be to open the hood and watch the engine while shifting through from say park to reverse, neutral to drive, etc. Set the park brake and hold your foot on the brake pedal. Watch for excessive engine movement, especially while applying some light throttle briefly while FIRMLY holding the brake pedal. Please, be carefull. Don't let the car lurch forward or backward.

It has approx 98K once the car is warmed up and I have been driving,the problem doesn't usually occur.