Abstract: In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies.With this method,semi-infinite soils can be considered as an transverse isotropic half-space,its material functions varying with depth.Dividing the half-space into a scries of layers in the direction of depth,the material junctions in each layer are simulated by exponential functions Consequently,the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used.We have obtained the relationship between the "layer forces" and "layer displacements".This finite layer method,in fact,can also be called a semi-analytical method.It possesses those advantages as the usual semi-analytical methods do,and can be used to analyse the problem of the interaction between soils and structures.