Andrei Dmitrievich Kriachkov was born on November 24, 1876, in the village of Vakhrevo, Rostov district, Yaroslavl province, in the family of peasant Dmitry Iosifovich Kriachkov. After his father's death, when Andrei was six years old, he was raised by his grandfather, with whom he helped in the household. In 1888, he graduated from a three-year school in the village of Ilyinskoye on Belyna and was sent to his uncle in Vyborg, where he began working in the office of a tobacco factory. In 1890, he entered the Vyborg Real School, where he studied Swedish and Finnish languages, and graduated in 1896.

In 1897, Kriachkov entered the Emperor Nicholas I Institute of Civil Engineers. During his studies, he interned in various regions, including the Volga region and Crimea, and worked in the St. Petersburg city administration. In his final years, he received a scholarship and, after graduating from the institute in 1902, was required to work for three years in the provincial Construction Department. He chose the Tomsk provincial government and began working as a junior engineer, temporarily performing the duties of provincial architect. In 1903, he was appointed a teacher of architectural design at the Tomsk Technological Institute.

In November 1905, Kriachkov became the architect of the West Siberian Educational District, as well as of Tomsk University and the Technological Institute. He oversaw the construction of various buildings, including hospital clinics and institutes. In 1907, he went on a six-month business trip to Europe, visiting Germany, France, and Italy.

On February 29, 1916, Kriachkov was promoted to court advisers. In 1920, he became a professor, and in 1924 and 1928, he worked in the construction commission of Sibrevkom. In 1930 and 1936, he continued to combine work with teaching at the Tomsk Technological Institute and the Siberian Construction Institute. In 1926, he was a delegate to the All-Union Congress on Civil and Engineering Construction.

Since 1934, Kriachkov headed the Novosibirsk branch of the Union of Architects of the USSR. In 1937, his projects were presented at the World Exhibition in Paris, where they received the Grand Prix and a Gold Medal. Andrei Dmitrievich Kriachkov passed away on August 25, 1950, in Sochi, where he was buried. His burial place is considered lost.