Violent drillstring vibrations in a well should be suppressed to prevent premature failure of the drillstring parts and borehole wall and enhance the drilling process. This paper presents novel centralized impact dampers and torsional vibration dampers for lateral and torsional stick–slip vibration suppression which will function well in the harsh environment in the well due to their all-metal construction. A drillstring vibration model is used in this paper to simulate coupled lateral and torsional vibrations of the drillstring with impact and torsional dampers installed in the drill collar (DC). The high-fidelity model utilizes Timoshenko beam finite elements (FEs) and includes stress-stiffening effects to account for the gravity and axial loading effect on the transverse string stiffness. The rotational motions of the impactors result from dry friction tangential contact forces that occur when they contact the DC or sub. The tangential forces utilize a nonlinear Hertzian contact restoring force and a nonlinear, viscous contact damping force, in place of the typical coefficient of restitution (COR) model that cannot provide the required normal and tangential contact forces. The primary conclusions drawn from the simulation results are: (1) both the lateral vibration of the drillstring that is close to the bending critical speeds and the vibration induced by destabilizing forces can be suppressed by impact dampers and (2) the torsional stick–slip motion of the drillstring can be mitigated by the torsional damper.