The UNI-Y is the University Students' Wing of YMCA. Any University student of good character, irrespective of religion and gender, who has completed his school and is doing any course recognized by a university comes under the category of students and are eligible for UNI-Y membership. However these students can claim membership only up to the age of 25 including grace period.

As the mighty oak exists in its sapling so does a man in the child. This is a profound truth not a mere analogy. The sapling sprouts only if the seed is sown. The seed was sown in the year 1959 when the YMCA Forum for Public Affairs in Hyderabad under the inspiring leadership of its Chairman, Mr. Justice Gopalrao Ekbote, organized the First Model Assembly, during which a decision was taken to have a forum for young students as well.

The seed sprouted in the year 1963, when the Second Model Assembly was held and the first UNI-Y came into existence at Hyderabad. There were only three members including Mr. D.S. Chinnadorai, General Secretary, YMCA Hyderabad, when UNI-Y began. Ever since its formation the number of members steadily increased thanks to the enthusiasm of the leaders and members. The second UNI-Y was started in Nagpur followed by the third unit in Secunderabad and soon several others followed. The sapling, which had grown to be a plant, started blossoming by the time of the Fourth Model Assembly as the UNI-Y witnessed a phenomenal growth.

The UNI-Y emblem is an inverted red triangle with a flaming torch in the middle. The three sides of the triangle denote Friendship, Cultural pursuit and Social action. The torch with the name 'UNI-Y' inscribed on it represents the eternal dynamic spirit of the youth.