The Ulams were a wealthy Polish Jewish family of bankers, industrialists, and other professionals. Ulam's immediate family was "well-to-do but hardly rich". His father, Józef Ulam, was born in Lwów and was a lawyer, and his mother, Anna (née Auerbach), was born in Stryj. His uncle, Michał Ulam, was an architect, building contractor, and lumber industrialist. From 1916 until 1918, Józef's family lived temporarily in Vienna. After they returned, Lwów became the epicenter of the Polish–Ukrainian War, during which the city experienced a Ukrainian siege.