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A brief state-of-the-art about vertical ground motions is compiled. Recommended provisions to include the vertical ground motion in the seismic design of structures available in some international building codes are discussed. The vertical component of the ground motion recorded near the source (epicentral records) in earthquakes originated in the subduction zone of the Mexican Pacific Coast is studied. The curves for the spectral displacement ratios of vertical to horizontal components are analyzed and adjusted to an envelope function for the mean response. Artificial records obtained from the proposed spectral intensity functions are compared with the records that gave rise to them. Furthermore, the design spectra proposed by some seismic codes in Mexico to account for the vertical effects are compared with the forecast spectra obtained from the horizontal spectral intensity with the described envelope function. Finally, qualitative recommendations for the election of the spectral design intensity in the vertical direction are provided.