Hydro dynamically developing and simultaneously (hydro dynamically and thermally) developing laminar flows of a Bingham plastic in a circular pipe have been investigated numerically. Solutions have been obtained by using a four-step fractional method combined with an equal order bilinear finite element method. For the hydro dynamically developing flow, shorter entrance length is required to reach fully developed velocity field for larger yield stress and non-monotonic pressure drop along the pipe centerline is observed when the yield stress exceeds a certain critical value. For the simultaneously developing flow, the heat transfer characteristics show the same trends as those predicted for the thermally developing flow (Graetz problem).