In scanning pages with double-sided printing, often the printing on the back-side shows through in the scan of the front-side because the paper is not completely opaque. This show-through is an undesirable artifact that one would like to remove. In this paper, the phenomenon of show-through is analyzed using first physical principles to obtain a simplified mathematical model. The model is linearized using suitable transformations and simplifying approximations. Based on the linearized model, an adaptive linear filtering scheme is developed for the electronic removal of show-through using scans of both sides of the document. Experimental results demonstrating the effectiveness of the method developed are presented.