Cubic lattice Monte Carlo simulation studies were conducted to examine the effect of confinement on dilute and non-dilute solutions of polymer chains in a channel with a square cross section. In dilute solutions, the partition coefficient K-c with channels of different widths d followed the scaling-law prediction, and was close to the square of the partition coefficient K-s with a slit of the same d. The chain with its bulk radius of gyration greater than similar tod/2 adopted a conformation extending along the channel and, with a decreasing channel width, the chain ends were forced to face outside. The chain conformation in broader channels was a compressed random coil. The K-c increased with an increasing polymer concentration phi(E) in the exterior solution equilibrated with the channel. In a weak confinement, K-c closely followed K-s(2) of the same phi(E) and d. The chains contracted at higher concentrations as they did in the bulk solutions. In a strong confinement, K-c was smaller than K-s(2) at the same phi(E) in the semidilute regime, and, at higher concentrations, sharply increased to the value close to K-s(2).