Just before the outbreak of World War Two, Dr Benckendorf, an anti-Nazi German scientist, is spirited out of Germany by a mysterious individual known as the Shadow, said to be responsible for dozens of similar rescues of creative, scientific and humanitarian figures.

At Cambridge University, Professor Horatio Smith, a brilliant but absent-minded archaeologist, invites some of his students to accompany him on a dig in Germany. Once there, they spend the night at a hostel on the Swiss-German border. A shot is heard and a man makes his way to the hostel, where a whistled signal alerts him to the presence of a second man, who helps him inside. German soldiers arrive but, finding nothing, conclude that their quarry has fled over the border.

General Von Graum, obsessed with apprehending the Shadow, interrogates Sidimir Koslowski, editor of a Polish newspaper. He had been present at the rescue of Benckendorf, but refuses to give any information about the Shadow.

Smith receives an invitation to attend a ball at the British Embassy in Berlin. He arranges to meet his students at the station the next day so that they may travel there together. When asked what he intends doing in the meantime, he gives a characteristically vague and uninformative answer.

Karl Meyer, a great pianist, is being used as slave labour at a concentration camp with several other prisoners. The guard threatens to use brutal measures to make them work harder, and makes his point by shooting at one of the scarecrows. Unseen by all, blood trickles from the scarecrow's sleeve.

Next day on the train the students discuss the Shadow's latest daring feat - the rescue of Meyer. Reading in the newspaper that the Shadow, dressed as a scarecrow, had been shot during the escape, they suddenly notice that Professor Smith's wrist is bandaged. He admits that he is the elusive Shadow, engaged in the systematic rescue of those whose intellect and commitment to freedom is vital to the future of civilisation. They salute his heroism and offer their assistance.

Von Graum discovers a torn corner of Smith's Embassy invitation in the scarecrow's discarded coat and realises the Shadow will be at the ball. He attends in the company of a beautiful female spy. She finds Smith suspicious, and confides her suspicions to Von Graum.

That night, she enters Smith's room and tells him that her real name is Ludmilla Koslowski, daughter of the Polish editor. Her father is now in a concentration camp and Von Graum has threatened to have him killed if she does not help find the Shadow. Smith decides that the Shadow's next task is to free her father and four German contributors to his newspaper.

Ludmilla tells Von Graum she no longer suspects Smith, but he realises she is lying. The following day, Smith and his students, disguised as pro-Nazi journalists touring the camps, overpower the commandant and his guards and smuggle the prisoners out. Gestapo soldiers search Smith's accommodation at the dig site, but do not find the carefully concealed refugees.

The students leave for England, taking with them several packing cases, over which they keep watch in an obviously suspicious manner. When the train reaches its destination waiting Nazi officers open the cases, which are found to contain relics. In the confusion, the refugees, who had been disguised as passengers, leave the train and make their way calmly over the Polish border.

Smith returns for Ludmilla. They flee together, but Von Graum is waiting for them at the border. Ludmilla is allowed to go free if Smith gives himself up. He complies, calmly informing Von Graum that though the Nazis may seem invincible they are in fact doomed, not in spite of their lack of mercy and thirst for conquest but because of it. Von Graum marches him to the border in the hope that he will attempt to run and can therefore be shot attempting to escape. But Smith is able to distract him just long enough to slip away unseen. As Von Graum fires impotently into the darkness the Shadow's whispered voice is heard pledging to return - and this time not alone.