The crack propagation of hydraulic fracturing of coal is actually a fracturing problem of semiinfinite 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 threedimensional equilibrium equations and constitutive equations of a homogeneous, isotropic linear elastic body. The exponential matrix is discomposed in order to avoid nonconvergence in solving directly the transfer matrix differential equations. The relations between the displacements and the stresses on the surface of semiinfinite body are obtained in introducing the infinite boundary conditions. The displacements and stresses in an arbitrary point of the semiinfinite 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 semiinfinite body.