The cross section for the elastic scattering of slow electrons by molecular hydrogen is calculated by use of the variational methods of Hulthén and of Kohn, full allowance being made for electron exchange. The trial wave function is assumed to have a form which in spheroidal coordinates resembles the analogous functions in spherical polar coordinates used in discussing elastic scattering by hydrogen and helium atoms. Quite good agreement is obtained with observed data - an agreement which disappears when exchange is neglected; this is a situation similar to that which arises in the case of helium.