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A new model for investigating the electrical tree growth in solid insulation using a hyperbolic needle-to-plane gap is presented. The needle is embedded in the insulation medium. Classification of tree shape depends on the electric field value is presented. Then, accurate computation of the electric field is a pre-requisite for calculating electrical tree growth. The electric field distribution is obtained from Laplace's equation by treating the tree structure as an extension of the stressed electrode i.e., conducting medium. The electric field is redistributed during each growth of the electrical tree. This is achieved by using the charge simulation method. The charge at the needle surface is simulated by a group of ring charges. To determine the appropriate arrangement of simulating ring charges inside the needle, a genetic algorithm is used. A number of series finite line charge is used for simulating the charge over each branch and sub-branch during the treeing progress. The presented model for simulating electrical tree growth is a three dimensional field problem. The used needle tip radius was 3 Â¿m while the gap spacing varied from 0.3 to 15 mm. The results have been assessed through comparison with available analytical and experimental data.