Abstract: Third order RungeKutta time splitexplicit scheme is generally used in nonhydrostatic atmospheric models. The stability and error of this scheme is analyzed in this paper. The amplification matrix of the scheme is of high order and high power. The derivation of its eigenvalues formula is performed with the Wolfram Mathematica software which handles complex symbolic calculations and a numerical test of onedimensional linearized soundadvection equations is performed to show the performance of this scheme. The Taylor series expansion of the norms of the eigenvalues is performed with higherorder terms kept and the splitting error term is derived out for both upwind and centered spatial differences. The splitting error and its relationship with the number of small time steps are shown directly and quantitatively. It is demonstrated that the scheme is numerically stable and has a smaller splitting error than secondorder RungeKutta time splitexplicit schemes. The splitting error term of centered spatial differences has higher order and so the split error is smaller than that in upwind schemes. These conclusions are also demonstrated by the analysis of the eigenvalues of propagating sound waves with different wavelength and the sound wave advection numerical experiment for the secondorder centered spatial difference with the RK3 splitexplicit scheme for which there are almost no differences in the forward and the backward moving mode. Moreover, The splitting error of the RK3 splitexplicit scheme is also smaller than the AdamsBashforthMoulton scheme. 