The flow of Maxwell dusty fluid over a stretching surface with variable thickness subjected to a magnetic field are considered. We consider the viscous dusty fluid, where the velocity of the dust particle is everywhere parallel to that of the fluid with velocity magnitude of the fluid is constant along each individual streamline. Also it is assumed that density of the dust particle is constant and the dust particles are uniform in size and shape and bulk concentration of the dust is small. The governing partial differential equations are transformed to a system of ordinary differential equations. These equations are solved numerically by RKBS-45 method. The effects of various physical parameters such as magnetic parameter, fluid particle interaction parameter, and wall thickness parameter are presented and discussed. The comparison with previous results shows an excellent agreement.