Engine/transmission noise in shifting to drive mode

My BMW 2005 328xi (51000 miles)vibrates and makes a correposning noise when I shift from NEUTRAL to DRIVE. When I shift to NEUTRAL or PARK mode, the noise/vibration subsides. Is this cause for concern ? What can be the cause?

Without being able to hear the noise ourselves, everything will be speculative.
With that in mind, I am going to speculate that you may be hearing the noise and feeling the vibration from a loose heat shield on your exhaust system.

However, I could also be totally wrong. The car needs to go to a mechanic who can observe and listen as the transmission is shifted into Drive.

Is this cause for concern ? What can be the cause?

Yes…my trucks make noise in the drive shaft, but have never felt a vibration. Friends 3 series BMW is smooth as silk. Have it checked, hopefully something minor.