Using a thin-layer method enhanced by continued-fraction absorbing boundary conditions, dynamic responses of a layered half-space subjected to a series of constant and time-harmonic line loads moving at a constant speed are studied. The thin-layer method for moving line loads is formulated for plane-strain as well as antiplane-shear conditions and is verified by comparison of computed responses of a homogeneous half-space subjected to a single constant load on its surface against available analytical solutions. Next, time-harmonic loads on a homogeneous half-space are examined. The study continues with both constant and time-harmonic loads on a layered half-space. Finally, multiple constant and time-harmonic loads are considered. The formulation and results demonstrate the effectiveness and versatility of the method in problems of dynamic response of layered media to moving loads.