A.N. Somov came from a family of hereditary nobles. He received his education at the Naval Cadet Corps and was commissioned to the 3rd Fleet Crew in December 1841.

In 1853, he was elected as a candidate for the position of Voronezh district leader of the nobility and appointed director of the Voronezh prison charity committee. In 1855, he became the Voronezh district leader of the nobility. In 1856, Somov was appointed judge of the Voronezh joint court, and in 1857, he was elected guardian of the Voronezh civil department's half-company of prisoners. In 1858, he became a member of the Voronezh provincial committee on peasant affairs.

In 1861, Somov was appointed a member of the temporary commission for preliminary arrangements on peasant affairs and later became a member of the presence on peasant affairs. That same year, he received the title of chamberlain. In 1862, he was appointed senior candidate for the position of provincial leader of the nobility. In 1865, he was elected chairman of the Voronezh provincial zemstvo administration, and in 1867, he became an honorary justice of the peace for the Voronezh district.

From March 31, 1868, Somov served as the governor of Tver province.

In 1890, he was appointed senator in the heraldry department of the Senate, and in 1891, he was transferred to the 5th department, then to the combined presence of the 4th and 5th land surveying departments of the Senate. Since 1896, he attended the 2nd general assembly of the Senate.

Somov was a lifelong honorary member of the Tver provincial charity for children's shelters.

In Voronezh province, he owned an estate covering 2552 desyatinas of land.

He passed away on October 31, 1899.