A study is made of Lamb's plane problem in micropolar viscoelastic half-space with stretch. The viscoelasticity is characterized by the rate-dependent theories of micro-viscoelasticity generalizing the classical Kelvin-Voigt theory. The displacement components, force stress, couple stress and vector first moment are obtained for a half-space subjected to an arbitrary normal load. Two particular cases of a horizontal force and a torque which are time harmonic have been considered. Several limiting cases are obtained as special cases of the present analysis.