Rodents explore the world by palpating objects with their whiskers. Whiskers interact with objects, causing stresses in whisker follicles and spikes in sensory neurons, which are interpreted by the brain to produce tactile perception. The mechanics of the whisker thus couple self-movement and the structure of the world to sensation. Whiskers are elastic thin rods; hence, they tend to vibrate. Whisker vibrations could be a key ingredient of rodent somatosensation. However, the specific conditions under which vibrations contribute appreciably to the stresses in the follicle remain unclear. We present an analytical solution for the deformation of individual whiskers in response to a time-varying force. We tracked the deformation of mouse whiskers during a pole localization task to extract the whisker Young's modulus and damping coefficient. We further extracted the time course and amplitude of steady-state forces during whisker-object contact. We use our model to calculate the relative contribution of steady-state and vibrational forces to stresses in the follicle in a variety of active sensation tasks and during the passive whisker stimuli typically used for sensory physiology. Vibrational stresses are relatively more prominent compared with steady-state forces for short contacts and for contacts close to the whisker tip. Vibrational stresses are large for texture discrimination, and under some conditions, object localization tasks. Vibrational stresses are negligible for typical ramp-and-hold stimuli. Our calculation provides a general framework, applicable to most experimental situations.