Shaking of Car While Parking

Describe the "shaking back and forth?" Do you mean it idles rough, or does the car move forward and backward slightly? I need more information to properly advise you. Ill check back on this post in a moment.

Thanks for your reply. Basically, it is a slight shaking for about 2 seconds.

How many miles does she have on her? Has the transmission been serviced? Any acceleration or performance issues that are noticeable? When was the timing belt last replaced?

I bought the car about weeks ago. It is on 110K miles. I did not encounter any acceleration or performance issues. Regarding the transmission, everything seemed fine. I did not see any transmission servicing in the carfax. I am not exactly sure when was the timing belt last replaced. Did not see any such thing in the carfax.

Your posting is a bit hard to understand and when someone asked for more specifics, you basically gave the same answer as your posting, so we are guessing here. From what I understand from your posting though, it sounds like you are not completely depressing your brake pedal and making sure the car is absolutely and completely stopped before you put the transmission into park. Any time you shift into or out of park and into any gear, you should have your brake pedal depressed as far as it goes before moving the gear anyplace. The will beat your transmission to death anytime.