The temperature coefficients and phase velocity dispersions of elastic surface wave layer mode with Ag or Pd layer on piezoelectric LiNbO3 svbstrate rotated 131$^{circ}$ Y out are calculated as a function of thickness by numerical method. Calculated results are shown that the temperature coefficients are rapidly increased in proportion as the thickness of Ag layer increases. and irregular variation of the temperature coefficients appears in the case of Pd layer. Minimum value, -36$ imes$10 /$^{circ}C$, of the temperature coefficients of elastic surface wave with Pd layer on LiMbO3 substrate rotated 131$^{circ}$ Y cut is obtained at wh=9000.