For the 58 Rajya Sabha seats to be filled, 33 candidates from 10 states have been unanimously elected. Voting for the remaining 25 seats is being held in six states: Uttar Pradesh, West Bengal, Karnataka, Jharkhand, Chhattisgarh and Telangana.
The Rajya Sabha vacancies next month include 17 from the Bharatiya Janata Party (BJP) and 12 from the Congress.
Three nominated members - actress Rekha, cricketer Sachin Tendulkar, and social worker Anu Aga -- will retire in April.
The BJP has filed 18 candidates for the biennial polls. They include Anil Baluni, the national head of the BJP's media wing, from Uttarakhand and Saroj Pandey, BJP general secretary, from Chhattisgarh.
Union Minister of Health and Family Welfare J.P. Nadda has filed nomination papers as the BJP candidate from Himachal Pradesh, Finance Minister Arun Jaitley will contest from Uttar Pradesh and Union Law Minister Ravi Shankar Prasad from Bihar.
The BJP has also fielded Union Petroleum and Natural Gas Minister Dharmendra Pradhan and Union Social Justice and Empowerment Minister Thawar Chand Gehlot from Madhya Pradesh for another Rajya Sabha term.
Union Minister of State for Road Transport and Highways Mansukh L. Mandaviya and Minister of State for Agriculture and Farmers Welfare Parshottam Rupala will contest from Gujarat.
In Congress, Naranbhai Rathwa and Amee Yajnik will contest from Gujarat and Dhiraj Prasad will contest from Jharkhand.
Akhilesh Prasad Singh and Lekhram Sahu will contest from Bihar and Chhattisgarh respectively, while Rajmani Patel, Kumar Ketkar, Porika Bairam Naik and Abhishek Manu Singhvi are contesting from Madhya Pradesh, Maharashtra, Telangana and West Bengal, respectively.
West Bengal Chief Minister Mamata Banerjee earlier said the Trinamool Congress would back Singhvi.
Mahendra Prasad Singh and Bashistha Narain Singh are the Janata Dal (United) candidates for the polls.
Counting of votes will begin from 5 pm onwards on Friday. Results are expected to will be announced the same evening. (ANI)