Continuous sediment has a wide application in chemical engineering process, such as wastewater treatment, water reuse, mineral waste manage and processing. This paper provides analytical solutions of the ideal continuous settling model by using the method of characteristics. The analytical solutions are compared with experiment data to show that the solutions accurately predict the sediment height and concentration as a function of time and loading conditions. Additionally, three alternative methods, using finite differences are compared to the analytical solutions, and their accuracy and efficiency are evaluated. It is shown that all three methods are reliable for solving sedimentation problems but have varying efficiency. Method YRD is the most accurate but also has the greatest computation and implementation cost. Method SG is the least accurate but is the easiest to implement with lowest computation cost. Method G is a compromise between the two methods, providing acceptable accuracy and low computation cost. (C) 2015 Elsevier Ltd. All rights reserved.