One serious problem in deep hole drilling is the occurrence of a dynamic disturbances called spiralling. A common explanation for the occurrence of spiralling is the coincidence of time varying bending eigenfrequencies of the tool with multiples of the spindle rotation frequency. We propose a statistical model for the estimation of the eigenfrequencies derived from a physical model. The major advantage of the statistical model is that it allows to estimate the parameters of the physical model directly from data measured during the process. This represents an efficient way of detecting situations in which spiralling is likely and of deriving countermeasures.