Marinos Carburis, a Greek from the Island of Kefallonia and serving as lieutenant-colonel in the Russian Army, offered to undertake the project. Carburis had studied engineering in Vienna and is considered to be the first Greek to hold a diploma in engineering.

Carburis directed workmen to wait for winter, when the ground was frozen, and then had them drag the large stone over the frozen ground to the sea for shipment and transport to the city. He developed a metallic sledge that slid over bronze spheres about 13.5 cm in diameter, over a track. The process worked in a way similar to the later invention of ball bearings. Making the feat even more impressive was that the labour was done entirely by humans; no animals or machines were used in bringing the stone from the original site to the Senate Square. After Carburis devised the method, it took 400 men nine months to move the stone, during which time master stonecutters continuously shaped the enormous granite monolith. Catherine periodically visited the effort to oversee their progress. The larger capstans took 32 men at once to turn, this just barely moving the rock. Further complicating the issue was the availability of only 100 m of track, which had to be constantly disassembled and relaid. Nevertheless, the workers made over 150 m of progress a day while on level ground. Upon arrival at the sea an enormous barge was constructed exclusively for the Thunder Stone. The vessel had to be supported on either side by additional two full-size warships. After a short maritime voyage, the stone reached its destination in 1770, after nearly two years of work. A commemorative medal was issued for its arrival, with the legend "Close to Daring".