This paper presents the results of a Finite Element Analysis (FEA) of the formation of the fracture trajectory during the detachment of rock masses depending on the mechanical parameters of anchoring, including in particular the depth of anchoring and the coefficient of friction of the anchor head against the rock. The analysis was carried out for the effective anchorage depth hef=50, 100, 150mm and the coefficient of friction of the anchor head against the rock = 0.15, 0.3, 0.45. The analysis showed that for the adopted anchorage depth range, the range of the potential extent of the failure zone, measured on the free surface, relative to the anchor axis, increases with its increment. On the other hand, the depth of anchoring, in the studied range of this parameter as well as in view of the assumed mechanical parameters of the rock, has no significant effect on the value of the angle of destruction cone 0 (in the initial phase of the destruction of the medium). For the value of the friction coefficient =0.15, there is a clear deep penetration into the fracture at its initial stage of development (at the initial angle of 0 = ~ -20°), promoting further spread of the fracture on the free surface. For larger values of the friction coefficient (=0.3 and 0.45)-the trend is less pronounced (α = ~ -2°÷-8°) resulting in a decrease in the crack range.