This paper describes a 3D quasi-static electromagnetic model for calculating the electric field strength of overhead power lines. The phase conductors and protective wires of overhead power lines are approximated by rectilinear thin-wire cylindrical conductor segments, which sufficiently accurately approximate the shape of a catenary. Metal poles of overhead power lines distort the electric field and can significantly reduce its value, so they are also taken into account by being approximated by segments of cylindrical conductors of zero potential. The system of linear equations for calculating the charge density distribution is obtained from the matrix of the eigen and mutual coefficients of all coupled components of the quasi-static electromagnetic model. The distribution of the scalar electric potential and the electric field strength at arbitrarily selected points in the air is calculated by solving a global system of linear equations. In a numerical example, the distribution of the electric field strength in the vicinity of a metal pole of an overhead power line is calculated.