The main goal of this study is to analyze the surface part of the karst and some underground characteristics of Eocene karst system. The Karst cavities are widespread in the Eocene forming the upper formation under the Quaternary cover in the Cheria syncline. Therefore, the karstfied zone requires new methods for estimating average depth of the karts cavities from structural, geometrical, and mechanical properties of fractured rock. In that way, statistical methods is very efficient for describing in detail the shallow part of karst cavities, when Eocene limestone outcrops at the surface in the center and northern of the basin. A stochastic analysis is carried out to evaluate the influence of correlations between relevant distributions on the simulated RMR values, also to simulate the cavity depth. The model is also used in Monte Carlo simulations. The statistical analysis showed that Rock Mass Rating (RMR) depends on the hydraulically and geomechancal parameters. Naturally it is always possible to simulate a cavity depth (PKR) by several hydraulically and geometrical parameters of fractures (uniaxial compressive strength; RC), Rock Quality Designation (RQD), Spacing fracture (E J), inflow per 10 tunnel length (D 10m.L), friction cording of the angle of the rock mass (C D-I.j), layer depth (Pc), average aperture to each group of the fracture (d i), average fracture frequency to each group of the fracture (f i), fracture depth (df i)), especially in the case of k non real fracture geometry. The study of the relations between geomechanical fractured rock and fracture geometry, we can simulate any cavity depth (PRK) in Chera syncline.