In drilling operations, it is important to have an estimate of the fracture gradient of certain formation, in order to being able to estimate the maximum mud weight required for the next section of the rock formation, before casing is placed. For this reason, Leak-Off tests are conducted to determine the maximum pressure that the new section of the well can support without fracturing or losing fluid, being made during the drilling phase of the well in formations immediately below each casing shoe. The purpose this study is to perform the numerical simulation of this test using a commercial finite element program to calculate the Leak-Off pressure, considering the pumping rate as an input data of the problem and pressure at the borehole wall as the answer. The work will address two cases: a permeable rock formation and an impermeable rock formation composed of salt rock. Thus, for studying a real analysis of a Leak-Off test in permeable and impermeable rock, it becomes necessary to use models that consider poroelasticity and creep, respectively. For the characterization of salt rock it was used a creep law of dual mechanism of deformation, which considers only the dislocation creep mechanisms: planar and undefined. The two-dimensional models were studied and analyzed under the assumption of plane strain. The hypothesis that the Leak-Off pressure is reached when the effective tangential stress is zero (estimated graphically), was considered. Finally, some cases were simulated to check the possible effects of changing the permeability and the influence of pressurized fluid in the calculation of Leak-Off pressure in the permeable rock.