Abstract: By means of half_space Mindlin. s elastic solutions and correspondence principle between elasticity and viscoelasticity, the viscoelastic solution of displacement, subjected to suddenly applied vertical force and given elastic volume strain and standard linear solid model distortion constitutive relations, is derived from the Laplace transform. The solutions in time domain is established by the inverse Laplace transform. Based on the viscoelastic solution of vertical displacement, the settlement formulas for the center and corner point of a flexible rectangular foundation made by homogeneous distributing load on rectangular area beneath the surface of ground are systematically inferred. A computation program is compiled based on the developed solutions. Finally, an example was g iven by making use of the presented method. The calculation results show that the new theory is feasible and applicable and can successfully predict the settlement of deeply buried foundation. And the results show that it is necessary to take account of viscoelasticity effect of semi_infinite half_space in the calculation of stress and displacement.