The steady flow viscosity η and the dynamic viscosity η′ of several linear polyethylene melts (190°C) were measured using the Weissenberg rheogoniometer and the Instron rheometer. In correlating the two viscosities, the use of Graessley's theory of viscosity in steady shearing flow in combination with the box distribution of relaxation times as suggested by Maruyamaet al.has been critically examined. The new approach discussed in this paper uses Graessley's functionsh(θ)andg(θ)in conjunction with the relaxation spectrumH(τ)derived from linear viscoelastic data using an iterative method. The required relation isη(γ̇)=∫H(τ)h(θ)g(θ)3/2τd ln τ,θ=γ̇τ/2;where γ̇ is the shear rate and τ is the relaxation time. Hereg(θ)=(2/π) [cot−1 θ+θ/(1+θ2)]andk(θ)=(2/π) [cot−1 θ+θ (1−θ2)/(1+θ2)2].A good agreement was obtained in all cases without involving any coordinate shift. The approach illustrated in this article enabled us to estimate quantitatively the effect of shear rate on the relaxation spectrum and also to estimate fractional contribution to the viscosity at a given relaxation time and shear rate.