To better understand the two-dimensional proppant transport problem in vertical fracture, we use the Method of Characteristics (MOC) to simulate one-dimensional sedimentation of suspensions by gravity. Literature survey and background about proppant transport are introduced first. The theory of sedimentation and MOC is then illustrated. The empirical Richardson & Zaki’s equation, modified with the discontinuous flux approximation, models the hindered sedimentation of uniform particles in a fluid. The characteristic velocity of concentration change is then calculated and the distance-time diagram is plotted for suspension sedimentation problems. Results are compared with existing experimental data to find the best-fit parameters of empirical exponent, n and maximum volume fraction, cm. The algorithm developed here provides a means for validating three-dimensional proppant transport simulators with literature results on 1-D gravity sedimentation of uniform, spherical particles in a Newtonian fluid under non-Brownian conditions.