The lower friction coefficient and superior mechanical properties of palladium (Pd) alloys make them potentially advantageous for use in high-precision instruments and devices that require long-term stable performance. However, the high cost of raw materials and experimental expenses result in a lack of fundamental data, which hinders the design of high-performance Pd alloys. Therefore, in this study, first-principles calculations are used to determine the lattice constant and elastic modulus of Pd. A model of dilute solid solutions formed by Pd with 33 alloying elements including Al, Si, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and others, is established. The mixing enthalpy, elastic constant, and elastic modulus are calculated. The results show that, all other alloying elements except for Mn, Fe, Co, Ni, Ru, Rh, Os, and Ir can form solid solutions with Pd. Alloying elements from both sides of the periodic table enhance the ductility of Pd solid solutions, with La, Ag, and Zn having the most significant effects, while Cu and Hf reduce the ductility of Pd. Differential charge density analysis indicates that the electron cloud formed after doping with Ag is spherically distributed, thereby improving ductility. After doping with Hf, the degree of delocalization around the atoms is maximized, indicating a strong ionic bond between Hf and Pd, which results in a higher hardness of Pd₃₁Hf. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00186.