A soft ellipsoid model for Gaussian polymer chains is studied, following an idea proposed by Murat and Kremer [J. Chem. Phys. 108, 4340 (1998)]. In this model chain molecules are mapped onto ellipsoids with certain shapes, and to each shape a monomer density is assigned. In the first part of the work, the probabilities for the shapes and the associated monomer densities are studied in detail for Gaussian chains. Both quantities are expressed in terms of simple approximate formulas. The free energy of a system composed of many ellipsoids is given by an intramolecular part accounting for the internal degrees of freedom and an intermolecular part following from pair interactions between the monomer densities. Structural and kinetic properties of both homogeneous systems and binary mixtures are subsequently studied by Monte Carlo simulations. It is shown that the model provides a powerful phenomenological approach for investigating polymeric systems on semimacroscopic time and length scales.