A kinetic network model is developed for the viscoelastic behavior of block copolymer melts with spherical microdomains. This model accounts for the variation in density of the matrix polymer segments from the domain boundary to the outer interphase boundary, with a non‐Gaussian segment distribution involving one new parameter. Rate terms consistent with this assumption are used to obtain expressions for the stress transients as well as steady‐state stress in uniaxial elongational flows. This model predicts an apparent yield stress at low strain rates, that is most sensitive to the new parameter a. Comparison of available data with model predictions indicates that increasing domain concentration is described by increasing values of a in the model.