Quasi-static approximation based on first-principles calculations was adopted to explore the effect of 33 alloying elements on the thermoelastic properties of Pt-based alloys. The elastic constants and moduli of Pt-based alloy Pt₃₁X were generally lower when rare earth elements (RE=Y, La, Ce, or Th) were dissolved in the Pt matrix, mainly attributed to the higher average bond length between RE and Pt. Pt₃₁X with X=Ta, Nb, V, W, or Mo showed lower average bond lengths and stronger electron localizations than pure Pt, resulting in higher Young’s moduli. Meanwhile, the temperature coefficients of the moduli for Pt₃₁X (X=Ta, Nb, V, W, and Mo) were lower in the Pt-based alloys because the average bond length increased slowly with the increase of temperature, among which Pt₃₁W showed the lowest value of -15.82×10^-5 K^-1. Therefore, W, Ta, Mo, Nb, or V are considered as the candidate alloying elements for improving the elastic stability.