The son of a bacteriologist, Richard Eurich attended Bradford Grammar School and then Bradford School of Arts and Crafts, under H. Butler. On moving to Ilkley with his family, Eurich was inspired to say, 'The first winter in Ilkley opened my eyes to the great beauty of landscape under weather conditions which in town were only a signal for putting on extra clothing...' In 1924 he studied at the Slade under Professor Tonks.

He began exhibiting at the NEAC from 1927 and in 1929 he came to know Sir Edward Marsh who introduced him to Eric Gill; their interest gained him his first one-man show at the Goupil Gallery. He also met Christopher Wood, who was to have a strong influence on his work. In 1934 he married and moved to Dibden Purlieu near Southampton.

During World War Two he served in the Royal Navy as a War Artist, painting the theme of survival at sea.

From 1949, he taught at Camberwell and illustrated Shell and BP Shilling guides. He became a member of the NEAC in 1943 and was elected RA in 1953. Best known for his marine, coastal and harbour subjects, he also painted numerous landscapes. His paintings are often both intricately detailed and vast in scope, and his narrative pictures are rich in incident.