Sokolow traveled to the Soviet Union in 1934 with musician Alex North, her companion of several years. Like many of her contemporaries, she believed the Soviet Union to be a new, free society that would be a beacon to the rest of the world, and she was eager to see what progress the Soviets had made in adapting modern dance for revolutionary purposes.

The Russian dance world, in turn, was curious about American dance, and Sokolow was invited to do a lecture-demonstration of the Graham technique. Wanting to emphasize her American identity, the organizers of the performance asked if they could call her Anna Smith, but Sokolow refused to hide her background, and her hosts were forced to content themselves with listing her name in the American alphabet.

Regarding the response of the Soviet audience, Sokolow later recalled:

My performance had something of the effect usually attributed only to gentlemen who pull rabbits out of hats.... The audience had never seen anything like it before. It was entirely outside of their experience. They sat mentally agape. Unheard of dancing! No pretty curved movements! No acrobatic pirouettes! They were amazed, bewildered, as any group of people must be who are steeped to their eyes in traditions of 400 years of "pretty" dancing.

Sokolow quickly realized that Soviet dance, which she had thought would be a powerful and striking revolutionary dance movement, was in fact merely propaganda or athleticized folk dancing. Over the ensuing decades, many Soviet dancers, chafing under the restrictions of Soviet artistic culture, would themselves seek greater artistic freedom in the West.