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This paper reports on some mathematical and numerical details of the application of the electric field integral equation (EFIE) method to the analysis of planar structures printed on multilayered substrates. Closed-form expressions for singular and hypersingular terms of the transverse electric field Green's dyadic (TEFGD) are identified so that they can be explicitly extracted out before solving the EFIE. The problems due to the presence of the hypersingular contribution, usually argued to preclude the application of the EFIE to planar structures, are solved. In addition, a low-frequency expansion of the TEFGD corresponding to a single layer substrate is carried out to recognize nonsingular electrostatic-type contributions that can eventually become very important for computational purposes.