Abstract: By use of the Fourier Inteoral Transform. the initial function solution of single elastic layer is derived. And then, using the recurrence method of matrixs,the analytical formulas are presented to study the displacements and stresses of layers sudjected to surface loading. No matter how many soil layers are there,it is not to solve simultaneous equations. According to these formulas,we draw up a computing program of micro-computer. The result of example show that the method provided is correct.