It is a well-known fact that an injection of the borehole fluids into surrounding porous rocks often results in fault reactivation,such as during hydrocarbon production from a reservoir, fluid injection for enhanced oil recovery, hot dry rock geothermal energy extraction, and waste disposal or carbon dioxide sequestration. However, no rigorously derived method for the description of spatial and temporal distribution of seismic events and for the estimation of the critical value of pore pressure of a porous rock sufficient for the generation of an microseismic has ever been developed. There a model developed within the context of Biot’s theory of poroelasticity is used to obtain the distribution of pore pressure, then the pore pressure is substituted into a Mohr–Coulomb failure criterion to predict the fault stability and the spatio-temporal cluster of microseismic events in a reservoir. in this model, the Biot system of equations is formulated for the radial symmetry case and is supplemented by the relevant boundary conditions, Then the solution is constructed analytically. A key advantage and the novelty of the proposed approach is it allows one to monitor an influence of pressure applied at the borehole within and surrounding reservoir and to predict the lower and upper bounds for the critical state of a natural rock, and it can be used in different reservoirs.