Astronomical observations have been documented in pre-Hispanic cultures. However, little is known about the astronomical heritage of pre-Hispanic societies in Venezuela, since there are no evidence of an ancestral material culture as other regions of Meso and South America, and these native Venezuelan groups lacked a written, alphabetic or ideographic language. There are innumerable petroglyph deposits in almost all regions of Venezuela, especially near Lake Valencia (Carabobo state) and those of the Andean foothills (Barinas state). By means of computerized simulation and archaeoastronomy techniques, the occurrence of a total solar eclipse is verified: in July 1, 577 at the Vigirima site; and another total solar eclipse at noon on May 16, 1398 at the Bum Bum site. It is concluded that the contemplation of the total eclipses of the Sun, must lead to the need for communication and recording, and lacking any type of writing, they drew the phenomenon, using the techniques and means at their disposal: engraving on rocks.