Two finite-difference schemes for the computation of incompressible Bingham fluid flows in pipes are proposed. The variational Duvaut-Lions inequality is used as a mathematical model. One of the difference schemes is an analogue of the well-known MAC (marker-and-cell) scheme on staggered grids, the second employs one grid for velocity approximation, and the other for all the components of the strain rate tensor. The convergence of finite-difference schemes and the iteration method are studied. The obtained results are compared with those known from publications. The proposed schemes were used to compute Bingham medium with an inhomogeneous yield stress.