Is it possible to install SSD with 6Gb/s in Mac pro Mid 2010? Is it possible to install Solid State Drive with 6Gb/s speed in Mac pro Mid 2010?
Yes it should be possible to install a SSD with SATA 6Gb/s.  

The MacPro5,1 was offered with a 512 GB SSD by Apple actually. The internal interface is limited to 3 Gb/s (which roughly translates to 300 MByte/s max) though. As a consequence you will not benefit from the faster transfer rate of the SATA III SSD.

The same is valid for MacBookPro6,1 and MacBookPro6,2.

SATA 6Gb/s is backward compatible with SATA 3Gb/s. Some features recently implemented in SATA 6Gb/s won't work if a respective device is attached to a SATA 3Gb/s interface (e.g. Isochronous Native Command Queuing).