Dear student,
The two epics composed during the Vedic age are the Ramayana and the Mahabharata. The Ramayana was written by Valmiki from 500 BCE to 100 BCE which was an important epic that dealt with Hindu life and culture. The Mahabharata was written by Vyasa in the early Gupta period (4th century CE) which is considered as the longest epic which can be ever written.
Regards