A theoretical study is made of the trajectories and of the changes in magnitude and direction of the wave vectors of magnetostatic backward surface waves with different frequencies propagating in ferrite-insulator-metal structures with different insulating layer thicknesses and magnetized by a linearly nonuniform static field. It is shown that both forward and backward magnetostatic surface waves (MSSWs) propagate in a waveguide channel, on one side of which MSSWs undergo mirror reflection and on the other side of which their propagation direction is rotated, independently of the thickness of the insulator in the structure. It is shown that when MSSWs propagate in a nonuniform field, the forward wave is converted into a backward wave and, under certain conditions, the backward wave is converted into a forward wave. Some features of the propagation characteristics of magnetostatic backward surface waves are determined.