After nearly 40 years climbing through the ranks of Union Carbide Corp., Chairman Warren M. Anderson is facing the greatest challenge of his professional life.

Following the horrifying reports of deaths and injuries from a poisonous gas leak at Union Carbide's pesticide plant in Bhopal, India, Anderson, who became chairman in 1982, left the safe confines of the company's Danbury, Conn., headquarters and boarded a commercial flight to India, where he was taken into custody by Indian police and charged with criminal negligence. Later he was released and flown from Bhopal to New Delhi, and state authorities sought his expulsion from the country.

A company spokesman said Anderson went to India for two reasons: to head a team that is investigating the cause of the accident, and to work with Indian officials to provide emergency assistance to victims and their families.

Experts say the way the company responds to the catastrophe will determine its image and the reputation of the chemical industry for years to come. "Damage control experts" said the company is trying to show that it is horrified by the accident, willing to compensate the victims, and investigating the causes thoroughly. The company is also striving to and reassure community and political leaders who worry that such an accident could occur at one of Union Carbide's domestic plants.

Union Carbide stock was the second most active stock on the Big Board yesterday, falling another 1 7/8 to close at 36 7/8. Despite the company's efforts to convince investors that it has the financial strength and insurance to satisfy claims, the stock has fallen more than 11 points this week.

Anderson's business associates and friends described him yesterday as a courageous man who has an excellent command of the technical aspects of the chemical business. They said he is the kind of leader who takes personal responsibility for the company's activities.

"He is a man who has a deep sense of morality, and I admire his courage in moving right to the scene of this difficult tragedy," said Hugh L. Carey, the former governor of New York, who has known Anderson for many years. "There is considerable hostility toward him in India , but he is there, on his own, putting himself at risk. There is no substitute for leaderhip and that is what he is exhibiting."

"Before I heard he was going to go over there, I knew he would do it," said John M. Henske, chairman of Olin Corp., who described himself as a close personal friend of Anderson's. "He is knowledgeable about plant operations and product toxicity, and I was certain that with his sense of personal responsibility, he would go over there.

"The personal anguish he must be going through now, for Warren, this has to be a personal tragedy . . . He is a very compassionate person."

A former Union Carbide employe who worked closely with Anderson said it was ironic that the company was involved in the tragedy in India because it has carefully and rigorously instituted stringent health, safety and environmental management systems that are applied to its plants all over the world.

But these systems failed, it is imperative to find out why, and Anderson has the technical knowledge to be able to determine the cause and understand what happened, the employe said.

A company spokesman said yesterday that Anderson, who has a law degree and is a member of the New York Bar Association, went to India because he wanted to have first-hand knowledge of the situation. "Due to time and distance, it is difficult to get information and he felt he should be there so that moment by moment, he is informed," the spokesman said.

Anderson, who has an undergraduate degree in chemistry from Colgate University, joined Union Carbide in 1945, starting as a salesman and working his way up in the chemical side of the business. He has had operating responsibility for divisions in Europe, Latin America, Africa and the Middle East.

Union Carbide, the nation's third-largest chemical company, had about $9 billion in revenue last year.