A simple method is presented for the estimation of the Linear viscoelastic relaxation spectrum from capillary viscosity data. For that purpose, a modified Leonov model is employed and the spectra and model parameters are estimated through nonlinear regression using measured steady shear viscosity data and extensional viscosity data calculated from Cogswell's method. Using the proposed methodology, the spectra of several resins were estimated and they were used in a Maxwell model to predict the linear viscoelastic properties of these resins. The predicted properties (storage and loss moduli and complex viscosity) were found to be in very good agreement with data from oscillatory shear measurements, thus supporting the validity of the estimated relaxation spectra.