An approximate quantitative theory of the positronium hyperfine pressure shift (HPS) is discussed. Adopting the approach of Adrian, the fractional shift Δ (R) is calculated as a function of the positronium–buffer gas separation R; the measured HPS is obtained by a thermal average of Δ (R) over R. A quantum mechanical averaging technique is used, rather than classical methods, in which the Boltzmann factor exp[−V (R)/kT], where V (R) is the intermolecular pair potential, is replaced by the positronium center-of-mass wavefunctions. The fractional shift Δ (R) is divided into two parts; a negative long range van der Waals contribution and a short range positive exchange contribution. It is argued that in the positronium center-of-mass approximation the short range contribution to Δ (R) is the same for both hydrogen and positronium and therefore existing calculations on hydrogen are utilized. Perturbation theory is used to obtain the long range contribution of Δ (R) and two models are used to evaluate the matrix elements that occur. In either model the long range contribution is related to the van der Waals interaction and can be obtained from a power series in R−1. A hard core potential model of the problem is solved exactly and predicts the HPS to be nearly temperature independent, a result essentially due to the long deBroglie wavelength of thermal positronium. Finally, the wave equation is numerically integrated with realistic potentials to find the positronium center-of-mass wavefunctions and the pressure shifts. Results of the numerical calculation also indicate a relatively small temperature coefficient of the HPS. The calculations of the positronium hyperfine pressure shift have substantially better agreement with measured pressure shifts than do calculations on hydrogen.