The hydrogen solubility properties were investigated with the aim of developing hydrides of Ti based alloys for hydrogen storage applications. The hydrogen absorption characteristics and the thermodynamics of the dissolved hydrogen in Ti0.42Zr0.08Fe0.50 were investigated in the ranges 0 less than or equal to P/bar less than or equal to 40 and 323 less than or equal to T/K less than or equal to 473 by pressure reduction method and compared with TiFe and Ti0.45Fe0.45B0.1. The hydrogen intake capacity at any particular temperature and hydrogen equilibrium pressure is larger in the a phase of Ti0.42Zr0.08Fe0.50-H compared to that in TiFe-H and nearly the same in the beta phase. The plateau pressure in Ti0.42Zr0.08Fe0.50-H at any temperature is slightly higher than that in TiFe-H. The absolute values of the relative partial molar enthalpy and entropy of the dissolved hydrogen in Ti0.42Zr0.08Fe0.50-H are comparable to TiFe-H. The relative partial molar enthalpy and entropy of hydrogen absorption decreases with the increase of hydrogen content in the a phase of Ti0.42Zr0.08Fe0.50-H and more or less remain constant in the alpha + beta phase.