The finitely extensible nonlinear spring chain model for polymer molecules in dilute solution is considered under the Peterlin approximation. A time‐dependent normal modes analysis is performed, and the equation governing the distribution of internal configurations is separated and solved. Both the integral and differential forms of the constitutive equation for the solution are obtained; they are expressed in terms of a set of eigenvalues that depend on the kinematic history of the material. The differential constitutive equation is similar to a multimode White‐Metzner equation. Material functions for steady shear, the inception of steady shear, steady uniaxial elongation, and the inception of uniaxial elongation, are calculated by solving a set of moment equations numerically. The results in the limits of very slow shear and very fast elongation agree quantitatively with results that are obtained without the Peterlin approximation.