Casualties and damages from earthquakes, which cannot be predicted, occur too often. Effective engineering of buildings using seismic‐resistant design is the primary method of mitigating these adverse effects. In this context, it is important to model the seismic excitation. It is known that because of the random characteristics of the phenomenon, it is difficult to elaborate such a model; therefore, numerous studies have been developed to fill some gaps and to improve the existing models in the literature. Based on this assumption, the present article has the objective of collaborating with these studies, proposing a numerical model for the simultaneous generation of the three components of seismic acceleration. The model was developed in the MATLAB (see Data and Resources) program and uses an evolutionary optimization method to determine the appropriate parameters of amplitude and frequency, of a relatively simple mathematical model, that allows generate the three components of seismic acceleration with predetermined characteristics (i.e., peak ground acceleration, duration of strong motion, and frequency content). The results show that the elaborated model is suitable for generation of the three components of seismic acceleration, which allows us to conclude that the model can be used for seismic engineering purposes.