How can I elongate my square shaped face?

Thank you for the images. 
Jaw augmentation can change the shape of your face with a chin implant (sizes vary) to enhance the shape and size of the face by elongating the size of the chin. You can ask your plastic surgeon more about these two options at your initial consultation. If you are unsure of the method that you would like to proceed with, look for an experienced, Board-certified facial plastic surgeon who implements advanced photo software system in their clinic, so you can see a 3D image of what you would potentially look like after the above mentioned procedures. 
Good luck! 

Without images, it is difficult to evaluate your specific situation. But one can alter the angles of the jaw and the height of the chin to fully alter the 'shape' of the face. It is called a 'V-line" approach in Asia but well practiced in North America by some of us. Talk to a Maxillofacial surgeon