We present a solution for the problem of wave scattering by an ice floe of variable thickness, modeled as an elastic plate which floats with negligible submergence. The solution method is based closely on the equivalent problem for an ice floe of uniform properties. We show that the solution for an ice floe of variable properties can be calculated straightforwardly from the solution for a uniform floe by expressing the natural modes for the variable floe in terms of the modes for a uniform floe. This in turn allows us to use the solution for the added mass and damping which has been calculated for the constant floe, for the floe of variable properties. Numerical results for various non-uniform floes are given and the effect of realistic thickness variations is investigated.