Switching events in inter connected power systems have significant effects on EHV transformers. Standard high-voltage lightning and switching impulse tests are performed on EHV transformers during manufacture, to ascertain breakdown strength of insulation used. But, during their service, transformers encounter numerous voltage transients of complex and varying wave shapes which do not necessarily resemble these standard surge type voltages. Transformers are complex assembly of coils around magnetic core having inductances and capacitances and therefore, exhibit unique frequency response characteristics with several natural resonate frequencies. Oscillatory overvoltages originating in power systems due to switching, faults and other phenomena often traverse through transformers and can excite one or more of the winding's natural resonate frequencies resulting severe internal voltage amplification and damage to insulation even when the terminal excitation voltages have relatively low amplitude. Adequate consideration must therefore be given to such low amplitude oscillatory transient voltages while designing insulation for grid connected EHV transformers. In this paper, the authors have analyzed the voltage stresses developed in the windings of a 400/220/33-kV grid connected transformer operating in the Eastern Regional Power Grid of India, when natural frequencies of the transformer winding are triggered by oscillatory switching transients. The developed voltage stresses have been compared with those under standard laboratory dielectric tests including newly incorporated fast front-long tailed switching surges.