The velocities and the wall effect for spheres and cubes in the accelerating region were compared experimentally for very high Reynolds number (18000NRe77000 for spheres and 12000NRe49000 for cubes). Experiments were conducted with 0.012, 0.015, 0.018, 0.021, 0.025, and 0.03175m spheres and their respective cubes of equal volume falling in water inside cylinders of diameters equal to 0.034, 0.049, 0.07, 0.10, 0.14, and 0.19m. The velocities of the spheres were always greater than the velocities for the respective cubes of equal volume. The wall effect increases with the particle size and fall distance. The relative wall effect between the spheres and the cubes varies with the fall distance and the ratio of the particle to tube diameter. The wall factor as a function of particle-to-tube ratio for the spheres is described well by the Munroe equation (5.7% absolute error), while for the cubes the points are more dispersed.