Abstract:The crack propagation of hydraulic fracturing of coal is actually a fracturing problem of semiinfinite layered media. It is necessary to discover a fundamental solution for layered coal, if the crack propagation of hydraulic fracturing is simulated by finite element or bunduary element method. A transfer matrix differential equation is derived from the threedimensional equilibrium equations and constitutive equations of a homogeneous, isotropic linear elastic body. The exponential matrix is discomposed in order to avoid nonconvergence in solving directly the transfer matrix differential equations. The relations between the displacements and the stresses on the surface of semiinfinite body are obtained in introducing the infinite boundary conditions. The displacements and stresses in an arbitrary point of the semiinfinite body are easily deduced by using the transfer matrix equation. The results derived here can be degenerated to the classic Mindline's solution in a semiinfinite body.