The simulations on equilibrium thermodynamic properties of short homopolymer chains, 3-, 4-, and 5-mer, by multicanonical Monte Carlo in a three-dimensional off-lattice model are quantitatively coincident with the exact analytical results of recently reported by Taylor [J. Chem. Phys. 114, 6472 (2001)], indicating that multicanonical algorithm is a permitted method in overcoming nonergodicity in observation of freezing transitions of single macromolecular chains. The investigation of freezing transition behaviors of 5-mer chains at ultralow temperatures reveals that four isomers coexist in the liquid state, then freeze into one of four isomers in the solid state depending on the bond length and bond fluctuation of the chain model after the occurrence of a liquid-to-solid-like first-order transition. (C) 2003 American Institute of Physics.