A study of earthquake seismicity is undertaken over the areas of Central and South America, the tectonics of which are of great interest. The whole territory is divided into 10 seismic zones based on some seismotectonic characteristics, as in previously published studies. The earthquakes used in the present study are extracted from the catalogs of the International Seismological Center, cover the period of 1900–2021, and are restricted to shallow depths (≤60 km) and a magnitude M≥4.5. Fore- and aftershocks are removed according to Reasenberg’s technique. The paper confines itself to the evaluation of earthquake occurrence probabilities in the seismic zones covering parts of Central and South America, and we implement the hidden Markov model (HMM) and apply the EM algorithm.