From 1912 to 1919 he studied at the School of Arts and Crafts in Stuttgart under Rudolf Rochga, and at the Stuttgart State Academy of Fine Arts under Christian Speyer, Christian Landenberger and Adolf Hölzel. In 1919, Elsas moved to Munich and took part in the New Munich Secession. With the support of his patron, Alfred Wolf, Elsas moved to Paris in 1928. From 1932 onwards, he and Pablo Picasso began experimenting with a new hand-printing process: Monotype Erwino. At the same time, he was also successful as a set designer, interior designer, commercial artist, and as a teacher at a painting school. From 1933 onwards, Elsas’ Jewish origins meant that he had no more chance of exhibiting in Germany.
He moved to Paris in 1938/39, where he joined the Union des Artistes Allemands Libres. Eugen Spiro was its chairman at this time, and was working to counter the art dictatorship of the German Reich. Elsas was active in the People’s Party of Léon Blum and became friends with Fernand Léger. In September 1939, Elsas was interned in the Chambaran camp in southern France, along with Willi Münzenberg, Leopold Schwarzschild and his friend Paul Westheim. After German troops invaded in 1940, Elsas was sacked and went into hiding in Ardèche, where he was hidden for a year by the inhabitants of the village of Le Cheylard. In 1944, Elsas returned to Paris. After the war, he was given French citizenship.