Pressure gradients have been measured for vertical flows of slurries of particles with diameters between 1.37 and 3.4 mm in pipes of diameter 26 and 40 mm. By expressing the wall shear stress as the sum of fluid and particle components, the wall stresses for the particles have been evaluated. The stresses increase with particle diameter and density, mean flow velocity and particle concentration. Measurements of the velocity of the particles closest to the pipe wall suggest that considerable distortion of the velocity distribution occurs, compared to that of the clear carrier fluid. The measurements confirm that a region of reduced particle concentration forms at the pipe wall, with coarse particles giving a pronounced change of this type. The wall stresses resemble those discovered by Bagnold for particles sheared in Couette flow. In Bagnold’s experiments, wall stresses were found to be strongly dependent on solids concentration. Since the particle concentration at the wall was unknown in the present investigation, a correlation for wall stresses has been obtained in terms of the mean concentration. The correlation can be used to estimate pressure gradients for vertical flows of nearly isometric angular particles.