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I think there are numerous 64 bit Ubuntu users who are suffering from the crash of Flash Player just like myself.  There is a better way to install Flash Player for 64 bit Linux than installing one from the Ubuntu repository and that is what I am about to write.  This is obviously not the perfect solution yet I think the best way to use 64bit Flash Player for now.  I hope Adobe will release a stable 64 bit Flash Player for Linux soon.  Anyway, here we go!

Adobe has released a preview version of Flash Player (Flash Player “Square”) for 64bit Linux.
http://labs.adobe.com/downloads/flashplayer10.html
http://labs.adobe.com/downloads/flashplayer10_64bit.html
http://labs.adobe.com/downloads/flashplayer10_square.html
At the bottom of the web page, you can find the download link.

Download plug-in for 64-bit Linux (TAR.GZ, 4.1 MB)

In my case, the latest alpha version of 64 bit Flash player does not work well (e.g. Video on youtube constantly freezes) yet the previous alpha one works better. So first, try the latest one and if it doesn’t work well, download the following one.

http://download.macromedia.com/pub/labs/flashplayer10/libflashplayer-10.0.d21.1.linux-x86_64.so.tar.gz
http://download.macromedia.com/pub/labs/flashplayer10/libflashplayer-10.0.45.2.linux-x86_64.so.tar.gz

Before installing it, if there is a previously installed Flash player, it has to be removed first.

To check it, open ‘Synaptic Package Manager’.
System -> Administration -> Synaptic Package Manager

Search by 'flash' and make sure neither flashplugin-nonfree nor flashplugin-installer is installed. If any of these are installed, remove first.

Extract the libflashplayer file downloaded to the firefox ‘plugins’ directory.
e.g.) If the file is in the /home/username/Desktop directory,

$ cd /usr/lib/firefox/plugins
$ sudo tar -zxvf ~/Desktop/flashplayer10_2_p3_64bit_linux_111710.tar.gz

To use this Flash player in other browsers such as Opera, create the symbolic link to the /usr/lib/firefox/plugins/libflashplayer.so file in the ‘/usr/lib/mozilla/plugins’ directory.

$ cd /usr/lib/mozilla/plugins
$ sudo ln -s /usr/lib/firefox/plugins/libflashplayer.so

If the file with the same name already exists, user ‘f’ option to overwrite it.

$ sudo ln -sf /usr/lib/firefox/plugins/libflashplayer.so

Now, open the Firefox and test if it works well.