An approximate solution of the contact pressure distribution of a bolt on the walls of holes of butted double-shear connection elements is obtained. The solution is presented in explicit form and is closed on the thickness of each of the butted elements of the connection. Comparison of the results of calculation of contact pressure on the proposed solution with experimental data, obtained by solid photoelasticity on optical models of connections, showed sufficient accuracy for this approximate solution for engineering calculations. The results can be used in calculations of the strength of bolted, riveted and articulated connections.