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Improper or inadequate insulation may lead to failure during impulse tests of a transformer. It is important to identify the type and the exact location of insulation failure within the winding of power transformers. This paper describes a new approach using fractal theory for extraction of features from the impulse test response of a transformer and Support Vector Machine (SVM) in regression mode to classify the fault response patterns. A variety of algorithms are available for the computation of Fractal Dimension (FD). In the present work, Box counting and Higuchi's algorithm for the determination of FD, Lacunarity, and Approximate Entropy (ApEn) has been used for the extraction of fractal features form time domain impulse test response. The analysis has been performed on both Analog and Digital Models of a 3 MVA, 33/11 kV transformer. A noticeable finding is that the SVM tool trained with the simulated data only is capable of identifying the location and fault classes of analog model data accurately within a tolerance limit of plusmn3.37% .