Comprehensive thermodynamic studies have been conducted for the systems V-H (246-554°), Nb-H (352-671°), and Ta-H (350-631°) in the pressure range 1-800 Torr by measuring the equilibrium hydrogen pressure as a function of composition. Each of these systems is comprised of a single solid phase in the temperature and pressure ranges studied. For each system a semiempirical equation, based on the statistical formulation of the simple interstitial solid solution model, is presented. The equations not only adequately reproduce the P-C-T data within the ranges of study but appear to be reliable to much lower temperatures. For example, they have been used to predict the T-C boundaries of immiscibility regions; for one system (Nb-H), for which comparison with an experimentally derived diagram is possible, agreement is very good. Calculated critical compositions, temperatures, and pressures are given. The partial and integral entropies and enthalpies of formation were calculated for the single-phase regions at 1 atom % intervals up to the maximum compositions of 34 (V-H), 39 (Nb-H), and 27 (Ta-H) atom % H. The results are compared in detail with those of other work.