Abstract We present scattered intensities and values of the electromagnetic field for p-polarized light on Ag grating surfaces using the theory of Toigo, Marvin, Celli and Hill. The theory is based on the application of the extinction theorem to Green's theorem. The program for calculations is set for any shape of the grating profile. Calculations are performed when the incident light is in resonance with the surface plasmon polariton. The shape of the scattered intensities are calculated for different grating amplitudes and it is shown that, for example, the reflectivity can present a minimum or a maximum depending on the amplitude and shape of the grating. It is shown that the enhanced field (the ratio between the modulus squared of the scattered field to the modulus squared of the incident field) (e) has a maximum when the reflectivity is a minimum as a function of the incident angle. The maximum of e is larger when the minimum in the reflectivity is smaller as a function of the grating amplitude. The value of e is calculated in a fine grid near to the grating and the values of the maxima are of the order of 250, then if the Raman cross-section is proportional to the fourth power of the field this could produce 104 to 105 in the cross-section and explain SERS. The width of the resonances as well as the plasmon dispersion relation will be also presented.