This paper proposes an innovative, generally applicable numerical model for the calculation of the three-dimensional (3D) electromagnetic field generated by high voltage (HV) overhead power transmission lines (OHL) on the buried metallic structures (e.g., pipeline networks). The numerical analysis is based on a coupled finite element-boundary element model (FEM-BEM) designed to calculate the induced potential on buried pipelines for complex geometrical structures of HV OHL networks working on normal or fault conditions. The one-dimensional (1D) FEM technique based on pipe elements is used to discretize the mathematical model that describes the interior of the pipe and is coupled with the mathematical model that describes the exterior of the pipe using 3D-BEM integral equations. The full electromagnetic field model gives the flexibility to calculate the potential distribution in any point of the soil, providing useful information for the step and touching voltages. The computation accuracy of the numerical algorithm implemented is verified through two test problems by comparing the numerical results with those obtained using a software package based on the Transmission Line Method (TLM) and CIGRE formulae. Last part of the paper presents calculations of the induced potential on buried pipeline in the vicinity of a complex HV OHL working on normal and fault condition. The influence of the currents’ direction and magnitude flowing on the HV OHL on the induced pipeline potential distribution is analyzed.