This study is concerned with the stress analysis of a rotating disc with a constant surface velocity. It is assumed that the mass of the disc is variable and is a function of time. Decrease in angular velocity causes angular acceleration and, therefore, shear stress field. Differential equations of motion for this case are solved analytically and shown that the present study is a generalization of the problem of a disc rotating with constant angular velocity. Stresses occurring in the problem are obtained for different values of surface velocity