A description of the MULTICOMP package is presented. The package was developed for multi-level modeling of polymeric materials and nanocomposites. The package includes a graphical user interface for material model construction, implementation of the modeling process, and analysis of the obtained results. For professional use, MULTICOMP supports the client-server architecture, which allows the transfer of resource-intensive calculations to remote computer clusters. As an example, the structure of the new Permeability module, designed to evaluate the gas permeability of thermoplastic polymers, is described. The new Nanoobjects module for creating models of nanoparticles and surfaces is also described. The results of using MULTICOMP to evaluate gas permeability, mechanical and thermal conductivity properties, and the performance of the package on various computing platforms are discussed.