We investigate the presence of topological twistons in crystalline polyethylene. We describe crystalline polyethylene with a model that couples the torsional and longitudinal degrees of freedom of the polymeric chain by means of a system of two real scalar fields. This model supports topological twistons, which are described by exact and stable topological solutions that appear when the interaction between torsional and longitudinal fields is polynomial, containing up to the sixth power in the fields. We calculate the energy of the topological twiston, and the result is in good agreement with values obtained using numerical simulation methods.