Isaac Bachrach was born in 1904 in the city of Dvinsk in Vitebsk Province (present-day Daugavpils, Latvia), in a Jewish family.
Isaac made his journalistic debut in the newspaper Vitebskie Izvestia at the relatively young age of sixteen.
In the early 1920s, Isaac Bachrach moved to Moscow, where he began to study at the Faculty of Literature of Moscow University. During his studies, he was a prolific contributor to Moscow newspapers. It was then that he adopted the pseudonym Isbach (derived from the initial letters of his first and last names) and changed his first name to Alexander.
1925 saw the publication of Alexander Isbach's poetry collection Smena, the first of his many published titles. Isbach's works focused on the Red Army, and he also paid attention to its Jewish soldiers. He took part in the creation of several literary societies with a "proletarian" bent.
In 1934, Alexander Isbach graduated from the Institute of Red Professors – a higher educational institution that had been set up by the Soviet regime to train the Party's ideological cadres and social science teachers.
Following the Nazi invasion of the USSR in late June 1941, Alexander Isbach was called up to serve as a military correspondent. In the course of the war, Isbach served on the Northwestern Front in the newspaper Za Rodinu, and on the 2nd Belorussian Front in the newspaper Frontovaya Pravda. He attained the rank of Major of the Supply Service. Isbach was awarded the Order of the Red Star (1942); the Order of the Patriotic War, 2nd class (1943); the Order of the Red Banner (1945), and some medals.
After the end of the war, Alexander Isbach returned to Moscow and resumed his literary activities. By that point, he had become a professor at the Maxim Gorky Literature Institute.
In 1948, Isbach published a collection of autobiographical stories titled Gody Zhizni [The Years of My Life], where he described his childhood in the shtetl. While offering some criticism of the rich Jews, the text also contained prayers and accounts of Jewish rituals, and it described the creation of a Zionist circle. At the height of the campaign against the "rootless cosmopolitans", such a collection could not be passed over in silence. In 1949, Isbach was accused of being a bourgeois nationalist and a Zionist, and sentenced to ten years of penal labor.
In 1954, a year after Stalin's death, Alexander Isbach was released from the camp. He was rehabilitated and allowed to resume his work as a teacher and writer. However, his health was undermined by the five years of harsh camp life.
Isbach continued writing autobiographical stories. Some passages from these texts – e.g., the lyrics of "Hatikvah" from the story "The Son of Honor" – were excised by the Soviet censors. Nevertheless, he remained a frequently published author. He was also regarded as one of the foremost experts on contemporary French literature.
Alexander Isbach died in Moscow in 1977.