Sony is a little bit different than most notebooks in that the correct Sony model number is not on the base of the laptop.
Correct Model Number
The correct and more useful Sony Vaio model number can typically be found next to the LCD screen, or on the plastic panel above the keyboard, as shown below. In this example we have a VGN-FS series notebook.
Incorrect Model Number
There is another "model number" on the underside of the laptop computer, but this is not helpful in most cases for finding parts or accessories.