In this paper, a 3D quasistatic numerical algorithm for computation of the electric field produced by overhead power lines is presented. The real catenary form of the overhead power line phase conductors and shield wires is taken into account with an arbitrary number of straight thin-wire cylindrical segments of active and passive conductors. In order to obtain more precise results of the charge density distribution, segmentation is conducted for each overhead power line span separately. Moreover, the presence of the towers which distort the electric field and significantly reduce its magnitude is taken into account. Therefore, the towers of overhead power lines are approximated using thin-wire cylindrical segments of passive conductors with electric potential equal to zero. From self and mutual coefficients of these components, system of linear equations for computation of the charge density distribution was obtained. In the numerical example, electric field intensity distribution in the vicinity of towers and under the midspan of overhead power lines is shown. In order to verify the accuracy of the presented model, the obtained results are compared with similar published examples and results available in the literature.