The propagation of a sinusoidal wave of small amplitude in an initially isotropic viscoelastic solid, which is subjected to a static pure homogeneous deformation, is discussed. The secular equation for a plane wave propagating an arbitrary direction with respect to the principal directions of the static deformation is derived. The complex slownesses corresponding to propagation along the principal axes of the static strain are found. Relations are obtained between these and the principal stresses associated with the static deformation, which generalize earlier formulas obtained by Ericksen for elastic materials.