The US Armed Forces and the Red Army only once met in battle. It was during the Russian Civil War that the Soviets and Americans fought each other directly.
Soviet Russia signed a separate peace treaty with the Central Powers, ending participation in WWI. Immediately, the Allies organized an expedition intended to regroup the Imperial Russian Army and subdue the Bolshevik revolution. Several contingents of Allied troops deployed to Russia.
The British regiment landed in Arkhangelsk, on the far northern tip of the Russian coast on August 2nd, 1918. The city held many supplies sent by the Allies to support the last Russian offensive against the Germans in 1917. Unfortunately, the supplies had already been seized by the Bolsheviks, who engaged the Allies in combat almost immediately upon their arrival.
The American contingent stationed in Arkhangelsk was dubbed the Polar Bear Expedition due to the position of the city near the Arctic circle. The freezing weather (as cold as 20 below zero) produced the nickname. Elements of the 85th division were sent by General Pershing to aid the British in Arkhangelsk. The principle U.S. combat unit so deployed was the 339th Infantry, comprised mostly of the Michigan National Guard, since dubbed The Polar Bears.
A report dated October 1919 stated that there were 210 American casualties; 110 KIA, 30 MIA, and 70 deaths from disease, mostly Spanish Flu. 305 were wounded.
The August issue of VFW Magazine contains an excellent, more complete account of this action by Earl Rickard, a Brown Water Navy veteran of Vietnam and freelance writer.