Abstract: By means of half-space Mindlins elastic solutions and correspondent principle between elasticity and viscoelasticity, the viscoelastic solutions of stress and displacement, subjected to suddenly applied vertical and horizontal concentrated forces and given elastic volume strain and standard linear solid model distortion constitutive relations, were systematically derived by Laplace transforms and Laplace inverse transforms.Finally, an example was given 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 deep buried foundation.And the results show that it is necessary to take account of viscoelasticity effect of semi-infinite half-space in the calculation for stress and displacement.This study provides a theoretical basis for calculating viscoelastic settlement of actual projects.