In this paper solutions are given for two problems on the motion of a dusty gas, using the formulation of Saffman [1]. The gas containing a uniform distribution of dust, occupies the semi-infinite space above a rigid plane boundary. The motion induced in the dusty gas is considered in the two cases when the plane moves parallel to itself (i) in simple harmonic motion, and (ii) impulsively from rest with uniform velocity. In case (i) the change in phase velocity and the decay of oscillatory waves are noted as functions of the mass concentration of dust f. In case (ii) the problem is solved by use of the Laplace transform, some velocity distributions are calculated for f=0·2, and it is shown that the shear layer thickness is decreased by the factor (1+f)−1/2 at large times.