Systems of dense polymers (that are concentrated in a cavity or a pore) can be modelled by self-avoiding walk models in confined regions of the lattice. Simulating these models using Monte Carlo algorithms poses challenging numerical problems, both with respect to the irreducibility and convergence of the algorithms. In this paper I give a short overview of the GARM algorithm and its implementation on lattice models of ring and linear polymers in confined squares or cubes. The implementations are based on BFACF elementary moves for lattice polygon models of ring polymers, and Berretti-Sokal elementary moves for self-avoiding walk models of linear polymers. In addition, a brief review of Flory–Huggins theory for analysing properties of these models as a function of concentration of the monomers is presented.