Both monopole and dipole acoustic logs measure the mode waves in the fluid of borehole. The shear-wave slowness of formation is obtained from the frequency dispersive curves of borehole. The SH-wave vibrates in the circumferential direction, and the shear-wave slowness is measured along the z axis for isotropy. There is no coupling wave of all P-wave and surface waves. It can be used to measure the shear-wave slowness to vibrate in the circumferential direction for anisotropy. It is different from sonic logging. For casing well, it is used to test the banding qulitity, when there is water ring, the tangential stress in the circumferential direction of the outer wall of the casing or the outer wall of the Cement Ring is 0, and the SH wave excited from the inner wall of the casing is cut by the water ring. SH wave can not continue to spread out and be reflected back into the solid (casing or cement ring), so that SH-wave in the radius direction reflected back and forth, along the z-direction become mode waves. When there is no water ring in the borehole wall, SH waves measured along the z-direction of the waveform are obvious different. In this paper, the SH wave is excited in the open hole or casing hole by axisymmetric excitation, and the calculation formula of SH wave is deduced by the method of real axis integration. The two-dimensional spectrum of SH-wave received along the z direction in the borehole wall is studied, and the two-dimensional spectrum distribution and acoustic waveforms of SH-wave in open hole and casing well are given. The propagation law of SH-wave in shaft wall is discussed. The structure of the probe for SH wave excitation and reception is briefly introduced.