In the United States
Death of a Salesman first opened on February 10, 1949, to great success. Drama critic John Gassner wrote that “the ecstatic reception accorded Death of Salesman has been reverberating for some time wherever there is an ear for theatre, and it is undoubtedly the best American play since A Streetcar Named Desire.” 
In the United Kingdom
The play reached London on July 28, 1949. London responses were mixed, but mostly favorable. The Times criticized it, saying that “the strongest play of New York theatrical season should be transferred to London in the deadest week of the year.” However, the public understanding of the ideology of the play was different from that in America. Some people, such as Eric Keown, think of Death of a Salesman as "a potential tragedy deflected from its true course by Marxist sympathies."
The play was hailed as “the most important and successful night” in Hebbel-Theater in Berlin. It was said that “it was impossible to get the audience to leave the theatre” at the end of the performance. The Berlin production was more successful than New York, possibly due to better interpretation.
Compared to Tennessee Williams and Beckett, Arthur Miller and his Death of Salesman were less influential. Rajinder Paul said that “Death of a Salesman has only an indirect influence on Indian theatre practitions.” However, it was translated and produced in Bengali as 'Pheriwalar Mrityu' by the theater group Nandikar. Director Feroz Khan adapted the play in Hindi and English by the name "Salesman Ramlal" played brilliantly by Satish Kaushik and with the role of his son portrayed by Kishore Kadam.
Death of a Salesman was welcomed in China. There, Arthur Miller directed the play himself. As Miller stated, “It depends on the father and the mother and the children. That’s what it’s about. The salesman part is what he does to stay alive. But he could be a peasant, he could be, whatever.” Here, the play focuses on the family relationship. It is easier for the Chinese public to understand the relationship between father and son because “One thing about the play that is very Chinese is the way Willy tries to make his sons successful." The Chinese father always wants his sons to be ‘dragons.’