First principles calculation based on density functional theory is used to comparatively investigate phase stability, elastic properties, and electronic structures of PdH and PdCuH phases with various H concentrations. Calculation shows that PdCuHx phases possess smaller heats of formation than corresponding PdHx as 0 <= x < 0.105, whereas PdHx phases are energetically more stable when x exceeds 0.105. It is also revealed that the volume expansion of PdCuH phase as a result of H addition is smaller than that of PdH at low H concentrations, implying that the alloying of Cu could lower hydrogen embrittlement of PdH. Furthermore, it is indicated that Cu should have an important effect of solid-solution strengthening in the Pd lattice, and the PdCuH phase has bigger E, G, and G/B values than PdH. The calculated results are discussed in terms of electronic structures, and are in good agreements with experimental observations in the literature. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.