The problem of mount bottoming of resiliently‐mounted equipment and its collision with adjacent structure when both are subjected to random vibration is solved in terms of probability of occurrence and the mean time between occurrences. The system is represented by two simple mechanical oscillators (with damping) whose relative motion is determined. A complete solution is obtained for white Gaussian excitation. This solution can also be applied to other structural problems, such as the mechanical design of electronic components, when the same representation can be used.