Stoch, the world number one who won the gold medal in Sunday's normal jump, suffered a bloody nose and left the course with his left arm in a sling.
"He's going to the village with a doctor, but he's OK," coach Lukasz Kruszek said.
The training session - which had already been delayed because of high winds - was cancelled.
Maksimochkin, ranked 40th in the world, fell awkwardly and was taken off the course on a stretcher as a precaution.
"He was taken to the hospital, where no serious injuries were diagnosed. But Maksimochkin will stay in the hospital until Thursday morning," the International Ski Federation said in a statement on its website.
The men are due to jump the large hill on Saturday.