The problem of collision between a simple mechanical oscillator (with damping) and an adjacent rigid member, or between two adjacent simple oscillators, when both are subjected to random vibration is solved in terms of probability of occurrence and the mean time between occurrences. A complete solution is obtained for white Gaussian excitation. This solution can be applied to such problems as the mechanical design of electronic components, bottoming of resilient mounts, and collision between an equipment item and adjacent structure, when the representations of a single degree of freedom system can be used.