Abstract: The natural fractures in deep carbonate reservoirs are developed, so in order to avoid borehole wall from fracturing which leads to serious mud loss, it is necessary to figure out the fracture initiation laws of the reservoirs. The poroelastic dynamics method was adopted to analyze the change of the stress field around the borehole by taking into account the change of borehole wall load and the flow of reservoir fluid in the process of drilling. Different from the traditional calculation method, this proposed model includes the time-dependent characteristics of stress field, the transmission of borehole wall load, the fluid-solid coupling and the effects of fluid and solid inertia. Then, a set of deep well parameters were taken as the examples to calculate the circumferential stress field. It is shown that the circumferential stress distribution is the same as the elastoplastic dynamic law. As the borehole wall load transmits into the reservoir in the form of elastic wave, however, the circumferential stress field calculated according to the poroelastic dynamics varies quickly with the time and then approaches to a fixed value after the dimensionless time \bar t=100 (2.87 ms). Finally, the borehole wall’s fracture initiation response to different bottom hole pressures was analyzed. It is indicated that when the bottom hole pressure is up to 135 MPa, fracture initiation of the borehole wall happens at \bar t=105 (3.01 ms). The fracture initiation of the borehole wall is rarely affected by the elastic modulus, and fracture initiation time and range are more affected by Poisson’s ratio. With the increase of Poisson’s ratio, borehole wall’s fracture initiation response to bottom hole pressure gets faster and the range of fracture initiation area increases.