We describe quantum-mechanical scattering calculations of re-vibrational transitions in H-2 induced by collisions with He. We use a close-coupled description of the dynamics which includes full re-vibrational coupling and a reliable potential energy surface. Rate coefficients for rotational and vibrational transitions in ortho- and para-H-2 are presented in the temperature range 10 less than or equal to T less than or equal to 5000 K.