The extraction and processing of many mineral ores result in the generation of large volumes of fine-grained residue or tailings. These fine sediments are deposited as a slurry with very high water contents and lose water after deposition due to self-weight consolidation. When the surface is exposed to the atmosphere they dry due to evaporation. In thin lifts deposition both processes, consolidation and drying take place simultaneously. The understanding and a quantitative description of both processes is important for the prediction of the dewatering process of fine sediments and tailings. A numerical model, which is able to simulate one-dimensional vertical flow due to consolidation and drying by evaporation of fine sediments, is implemented in a MATLAB code. The proper functioning of the model was verified for several combinations of boundary conditions, including a closed boundary, a constant flux boundary, a constant pressure boundary for both the top or the bottom and deposition of a fresh layer on top of a dried one. Subsequently the model was validated using data from experimental research on fine oil sand tailings. The model showed realistic outcomes for most boundary conditions and good correspondence with the observed behaviour in the drying and consolidation experiments. The paper describes the model, and the verification and validation simulations.