The vertical and horizontal displacements are obtained for a time‐dependent moving load on a viscoelastic half space. The load is assumed to increase exponentially with time and its velocity to decrease exponentially with time. The problem is solved as a quasistatic problem since the velocity of the load is small compared to stress wave velocities in the half space. The half space is characterized in shear by the four‐parameter model and is assumed to be elastic in its volumetric behavior. The elastic viscoelastic analogy is used in the solution of the problem.