An important aspect of the thermodynamic properties of chain molecules in solids is the amount of entropy that is associated with rotations about bonds. Of particular interest is the high‐pressure hexagonal phase of polyethylene. This system is modeled for the purpose of this calculation as an assembly of chains confined to small cylinders. This paper describes an integral equation approach to the problem that may be viewed as a continuum limit of the transfer matrix technique. Two cases are solved: (1) the freely jointed chain confined to a cylinder small enough to prevent the chain from folding back on itself, and (2) the fixed bond angle chain confined to the same type of cylinder. The result of calculation (2) is discussed in light of a model for the high‐pressure hexagonal phase of polyethylene.