Grounding grids (GG) play a fundamental role in the protection of personnel and prevention of damages in equipment during surge transients on substations caused by lightning discharges on power systems. In this context, a precise GG modeling must consider several factors such as the arrangement and the soil compacted in stratified layers. This paper proposes a lumped approach for GG buried in several stratified soils to compute the transient node voltages when subjected to lightning strikes. The vertical and horizontal electrodes are modelled separately by lumped circuit approach. The vertical electrode impedances buried in a stratified soil are computed by the numerical Method of Moments (MoM) in the full-wave electromagnetic software FEKOR , directly in frequency domain, and then, an electric circuit is obtained by the Vector Fitting technique. The horizontal electrodes are modelled based on the electromagnetic radiation theory, where each segment of the electrode can be regarded as a lamental currentcarrying conductor. Lightning currents of fast and slow-front waveforms, are employed in the simulations. Results show that when stratified soils are considered, the differences of the transient voltage peaks, in comparison with the ones calculated for the homogeneous soil is more pronounced as the thickness of soil decreases.