Objective: The objective is to obtain static and quasi-static deformation of a uniform half-space due to a center of rotation. Methodology and Results: The Galerkin vector approach has been used to calculate deformation field at an arbitrary point of an elastic half-space. Closed form analytical expressions for the displacements and stresses caused by a center of rotation buried in a homogenous, isotropic, perfectly elastic half-space are derived. The quasi-static deformation field for a viscoelastic medium has been obtained by applying the correspondence principle of linear viscoelasticity to the associated elastic solution. Explicit expressions giving the quasi-static deformation of a uniform half-space caused by a center of rotation are obtained when the medium is elastic in dilatation and Kelvin, Maxwell or SLS type viscoelastic in distortion. Conclusion: The explicit expressions for the displacements and stresses in an elastic and viscoelastic medium due to a center of rotation source have been obtained. Numerical results are shown graphically for displacements and stresses.