Abstract: According to wave motion theory,finite element mesh size satisfying the needs of engineering calculating precision is relevant to the upper limit of frequency range of random(response) problems.A new criterion of finite element mesh size——one third mesh size criterion——is(presented) according to wave motion theory.Taking high-frequency acceleration response analysis of simple support square plate as an example,the contrast between NASTRAN numerical results and the closed form solution reveals the effectiveness of this criterion in the high frequency random(response) finite element analysis.