The generation of accelerograms using stochastic methods has been a very useful methodology for solving the problem of the lack of appropriate strong-motion records for seismic design. Here, we propose the generation of synthetic strong motion for subduction earthquakes that present well-developed P waves and energetic arrivals of S waves associated with the main asperities of the source of these events. The first few seconds of these accelerograms are dominated by P waves; however, the strong motion is a mixture of S and P waves arriving at the same time. The traditional method considers only S waves. We propose to improve the stochastic generation of accelerograms taking into account a stratified velocity model, incident and azimuthal angles, free surface factors, and energy partition to incorporate the P and SV waves in the simulation. Finally, the simulated accelerograms are compared with the observed data recorded on rock by the Integrated Plate boundary Observatory Chile (IPOC) network during the 2007 Tocopilla and 2014 Iquique earthquakes. The use of P, SV, and SH waves in the stochastic simulation allowed us to generate three-component synthetic records. The early seconds are clearly associated with P waves, and the three components reproduce the shape and the amplitude in time and spectral domains for the observed and simulated records.