ABSTRACT Considering the configuration of bottom hole assembly (BHA), rock properties, effect of BHA rotation, and fluid damping, this paper presents a kinetic model for vibration analysis of drilling bits in vertical holes. Based on this model, it is demonstrated that drill bits undergo wobbling motion in drilling conditions. This model explains the lobed appearance of bottom hole patterns associated with PDC bit failure in hard rock drilling. Resonance is responsible for severe bit wobbling which may damage PDC bits rapidly in hard formation drilling. Sensitivity analysis with the model identifies possible solutions to the bit wobble problem: (1) using high-lateral-contact-area bits, (2) using full gauge near bit stabilizers and absorbers, (3) using high stiffness drill collars, (4) using heavy bits, (5) using low rotary speeds, (6) using high weights on bits, and (7) using viscous drilling fluids.