Abstract A simple model of linear polymer chains in porous media was developed, with model chains consisting of identical united atoms (beads) restricted to vertices of a simple cubic lattice. The macromolecules were confined between two parallel and impenetrable surfaces with a set of random obstacles. The excluded volume was the sole interaction among polymer beads (an athermal system). The model’s properties were determined with Monte Carlo simulations employing a Metropolis-type sampling algorithm with local changes of chain conformation. The mean dimensions of the chain were shown to depend strongly on the concentration of obstacles, while the polymer’s instantaneous shape remains constant. It was found that during migration in obstacle-dense environment the chain can be trapped in the region of local lower density of obstacles (a ‘cavity’), leave it after a period of time and move on to another cavity.