In this study, the collision of ice floes under the action of a monotonic wave is quantified. The lateral motion of an ice floe caused by the wave is modeled as the sliding of an object under gravity. In this case, the gravity component in the direction of motion varies with time and space as the wave progresses by the floe. Drag and added mass effects are included in the model. Two floes located at different positions are shown to have a net difference in their drift (caused only be repeated wave passages). In most cases, this differential drift eventually causes floe collision. When two floes collide, a spring and dash-pot model is adopted to calculate the contact force. A one-dimensional wave passing through a one-dimensional array of disc-shaped floes is examined. Two phenomena are apparent from the analysis. First, waves have a herding effect that forms bands of floes with the width equal to the wavelength. Secondly, the frequency of collision is sensitive to the elastic properties of the floes and the wave amplitude. With sufficient values of the damping constant, which operates when two floes collide, the floes stay in contact for prolonged periods, indicating the potential to freeze together and form composite floes, as was observed in the field studies.