Yes, you are eligible for Bank PO Post after passing B.E course but to get this post you need to appear and crack Bank PO Exam

Eligibility for Bank PO Exam:

Education
- You must have passed Degree with 60% marks in any discipline from a recognized University or any equivalent qualification recognized as such by the Central Government.

Nationality
- Must be either:
(i) a Citizen of India or
(ii) a subject of Nepal or
(iii) a subject of Bhutan or
(iv) a Tibetan Refugee who came over to India before 1st January 1962 with the intention of permanently settling in India or
(v) a person of Indian origin who has migrated from Pakistan, Burma, Sri Lanka, East African countries of Kenya, Uganda, the United Republic of Tanzania (formerly Tanganyika and Zanzibar), Zambia, Malawi, Zaire, Ethiopia and Vietnam with the intention of permanently settling in India

Age
- Must have attained 20 years and maximum 28 years