A vibration monitoring system operates down-hole in the bottom hole assembly above the drill bit. This system includes four spaced accelerometers which measure and differentiate between lateral, longitudinal and torsional drillstring vibrations. Three of the four accelerometers are in a cooperative spaced arrangement and measure tangential acceleration forces on the outer diameter of the drillstring for determining and measuring both lateral and torsional vibrations. The fourth accelerometer measures longitudinal vibration. Two embodiments are disclosed for arranging the three accelerometers which measure lateral and torsional vibration. In a first embodiment, the accelerometers are equi-spaced 120 degrees apart from one another. In a second embodiment, the three accelerometers are spaced 30 degrees apart from one another within a 60 degree arc. In both embodiments, all four accelerometers are positioned within the annular wall of a drill collar segment.