Positronium (Ps) collisions with molecular hydrogen are investigated theoretically. Elastic and Ps ionization cross sections are calculated. For elastic scattering the pseudopotential method, previously developed for rare-gas atoms, is applied. Ps ionization cross sections are calculated using the binary-encounter approximation. The results agree with swarm measurements at low collision energies and with beam measurements at higher energies. The total Ps-H 2 cross section when plotted as a function of collision velocity is close to the e −-H 2 cross section at velocities above the Ps ionization threshold confirming earlier observations [S. J. Brawley et al., Science 330, 789 (2010)]. However, below the threshold the two sets of cross sections are different because of the different nature of the long-range interaction between the projectile and the target, the polarization interaction in the case of e −-H 2 collisions and the van der Waals interaction in the case of Ps-H 2 collisions.