The stress‐growth phenomenon in the eccentric rotating disk (ERD) geometry is analyzed using a linearized Bird‐Carreau integral model. Good agreement is found between experimental observations and predicted responses for a low‐density polyethylene melt. Transient stress response is reported as time‐ and frequency‐dependent moduli. In start‐up, the approach of the viscous and elastic stresses to their steady‐state values at angular velocity Ω is found to be directly related to the decay of the storage modulus in stress relaxation after steady rotation.