Contact line dynamics occurs in wetting and dewetting phenomena. The dynamics of the triple line (line of contact of the gas, liquid, and solid phases) is considered for a Bingham fluid. The previous analysis of de Gennes for Newtonian fluids is extended, considering the moving liquid near the triple line as having a perfect wedge border. The velocity profile near the contact line is obtained along with the size of the plug flow region. The viscous dissipation is found by limiting the liquid thickness to a lower limit of molecular size. The relation between the triple line velocity and the dynamic contact angle is obtained; the result requires trial and error calculations, and is shown to yield de Gennes' equation as the Bingham fluid yield stress tends to zero. The requirement for the ideal wedge approximation is considered.