He created portrait busts, figurative groups, reliefs in wood, stone, marble, plaster, and bronze. In 1922, he began participating in exhibitions.[1]
In 1932, he made a statue to Andrey Sheptytsky, which was destroyed in 1945, but a plaster model was preserved.[1] On 25 July 2015, the statue of Metropolitan Andrey Sheptytsky, designed by Andrii Koverko, was installed and unveiled on 29 July 2015 in the square in front of St. George's Archdiocesan Cathedral.[3]
Among the main works:[1]
- series "Writers and Artists" (1922);
- new stone busts of Taras Shevchenko for the monuments to the poet in Lviv (1925) and Kolomyia (1929), which were damaged during the World War I; and busts of Mykhailo Voronnyi (1920s), Petro Kholodnyi Senior [uk] (1931); relief and bust of Ivan Franko (1926; 1940); plaquette "Josyf Slipyj" (1933);
- carved portraits of "Metropolitan Andrey Sheptytsky" (1931), "Dmytro Vitovskyi" (1933), "Ivan Franko", and "Oleksa Novakivskyi" (both 1943);
- easel figures "Head of an Angel" (1931), "Footballer" (1933), "Torso of a Woman" (1934), "Runner" (1936);
- made tombstones at the Lychakiv Cemetery on the graves of Ivan Lypa (1937), K. Rozhanska (1941), and Yaroslav Antonovych-Hordynskyi [uk] (1943);
- columns, a marble fountain, and a majolica stove with bronze allegorical reliefs for a coffee shop located in Lviv Town Hall (1941).
Other works:[1]
In 1952, Koverko's works, which were stored in the collections of the National Museum in Lviv, were destroyed.[4]