The Rouse model is a well established model for nonentangled polymer chains and its dynamic behavior under step strain has been fully analyzed in the literature. However, to the knowledge of the authors, no analysis has been made for the orientational anisotropy for the Rouse eigenmodes during the creep and creep recovery processes. For completeness of the analysis of the Rouse model, this anisotropy is calculated from the Rouse equation of motion. The calculation is simple and straightforward, but the result is intriguing in a sense that respective Rouse eigenmodes do not exhibit the single Voigt-type retardation. Instead, each Rouse eigenmode has a distribution in the retardation time. This behavior, reflecting the interplay among the Rouse eigenmodes of different orders under the constant stress condition, is quite different from the behavior under rate-controlled flow (where each eigenmode exhibits retardation/relaxation associated with a single characteristic time).