In order to determine the structure and dynamic properties of polymers systems in a random environment we developed and studied an idealized model. Properties of the model of confined linear and branched polymer chains were studied by means of the Monte Carlo method. Model chains were built of statistical segments and embedded to a simple cubic lattice. Then, the polymers were put into a tube formed by four impenetrable surfaces. A Metropolis-like sampling Monte Carlo algorithm was used to determine the static and dynamic properties of these model macromolecules. The influence of the size of the confinement (the tube diameter) and the chain length on polymer properties was studied. The universal behavior of confined polymer linear chains under consideration was found and discussed. The long-time (diffusion) dynamic properties of the system were also studied. The differences in the mobility of chains depending on the number of branches was shown and discussed – stars with an even number of arms exhibited the ballistic motion at certain conditions. The possible mechanism of the chain’s motion was discussed.