A full nonlinear regression program has been developed in order to determine the appropriate relaxation spectrum and set of material constants for a constitutive equation which can give the best fit to experimental data and predictions for a series of rheological material functions. The constitutive model used is an integral equation of the K-BKZ type suitable for polymer solutions and melts. Available experimental data for determination of the material parameters of the model were dynamic data (storage and loss modulus), steady shear flow data (shear viscosity and first normal stress difference), and steady elongational flow data (uniaxial, planar and biaxial elongational viscosities). The material parameters were determined by a nonlinear least-squares procedure based on the Levenberg-Marquardt method. The program was tested against experimental data of material functions for several polymer solutions and melts. A good fit was obtained between predictions and experimental data. Furthermore, predictions have also been made for unsteady (transient) material functions in shear and elongational flows using the parameters by best-fitting the model, and comparisons have been made with experimental data whenever available. In all cases, the predicted values were in good agreement with the experimental ones.