Yes it is possible. Male may not have penis. Causes of absence of penis by birth (congenital), accidental and one of uncommon cause is child penis may be chopped off to take revenge.

Recently I operated two cases. Both of them had birth defect, means they are normal male, with both testis but no penis.

TECHNIQUE----Large skin of size 13X17 cm. was taken from forearm along with nerves, artery and vein. A complete penis was constructed with urethra and left attached to forearm. Then in second stage it was detached from forearm and transferred to original genital site. Here nerves, artery and vein were anatomized. After 4 months penile implants will be inserted for erection of penis. Patients who are having functional testis can produce child. This penis will have sensation also.

Here are few pictures of Phallus construction