We report a second-order distorted-wave study for elastic electron-hydrogen molecule collisions in the low-and intermediate-energy range. In this study, the first-order T -matrix elements as well as the distorted wavefunctions were generated in the static-exchange potential of the ground-state target and a set of 18 pseudostates is used to calculate secondorder T -matrix elements. Differential and integral cross sections were calculated in the 1-40 eV scattering energy range. The comparison of our calculated results with some recent experimental and theoretical results is encouraging.