Geoparks consists of a number of adjacent geosites which have different attributes in terms of value (scientific, educational, aesthetics) and vulnerability. In the Lesvos Petrified Forest Geopark area, beyond the fossilized plants which constitute a natural monument of international value, there are many other sites of interest in terms of geology, geomorphology, ecology and local traditions. Coastal geosites of the Lesvos Petrified Forest are of significant geomorphological, aesthetic, educational and touristic value including cliffs, collapsed boulders, tafoni structures and cavernous weathering forms. Tafoni are widespread on the Miocene volcanic formations on Sigri coast. Miocene volcanics are hosting the silicified plants of the Petrified Forest; a protected natural monument of international value and beauty. Due to their importance and fragility the Natural History Museum of the Lesvos Petrified Forest adopted special measures for the protection and conservation of the tafoni structures of the territory. The research activity in the costal area of western Lesvos island led to the inventory of tafoni. As a consequence of the research some endangered tafoni were brought to the museum for protection, conservation and exhibition. This tafoni exhibition introduces the museum visitors to the processes forming the external surface of our planet.