The present article examines the chemical composition of fiber and shive from fiber flax and hemp obtained in Russia under industrial conditions, as well as that of the products of their alkaline delignification. Alkaline delignification was carried out at atmospheric pressure with a 4% sodium hydroxide solution; the chemical composition was determined via wet analysis. The chemical composition of hemp shive from Russian producers was studied for the first time. In the studied objects, the mass fraction of cellulose was found to range from 42.3 to 66.1%, and after alkaline delignification, the yield of products reached 47.0–50.0%. The behavior of fiber flax and hemp fiber is similar during alkaline delignification: cellulose content increases by 1.2–1.3 times, pentosan content decreases by 4.3–6.3 times, and lignin content is virtually the same. The behavior of fiber flax and hemp shive is dramatically different during alkaline delignification. The shive of fiber flax is resistant to alkaline delignification: cellulose content increases by 1.4 times, pentosan content decreases by 4.2 times, and lignin content increases by 1.4 times, which is due to the nature of lignin. Hemp shive is easily alkaline delignified: cellulose content increases by 1.8 times; the content of pentosans decreases by 5.8 times, and lignin content decreases by 2.2 times; the product of alkaline delignification contains cellulose (87.3%), pentosans (5.4%), and lignin (8.2%). The use of hemp shive for chemical and biotechnological transformation is expected to have high prospects.