This paper presents a one-dimensional flexural and longitudinal elastic wave propagation theory for analysis of ice floe impact with a rigid structure having a constant slope. In this paper, governing differential equations were derived following the Timoshenko beam theory which includes the rotary inertia and shear deformation of the ice beam, as well as the buoyancy effect of the water. The ice material was treated as a homogeneous, isotropic, and linearly elastic solid. Interactions between the longitudinal and flexural waves in the ice sheet, and the boundary conditions imposed by the rigid slope, have been considered. Solution procedures were developed based on the method of characteristics using a fixed grid finite difference approximation in both space and time. Computer solutions were obtained and plots were provided to show ice impact force-time histories and the wave propagation phenomenon for a range of floe impact problems of current interest. Comparisons were also made with other existing methods for calculating ice bending loads on sloping structures.