The　evaluation　has　been　made　for　normally　used　four　envelope　functions　of　earthquake　ground　motion.　Being　as　evaluation　standard　of　the　envelope　function　this　paper　point　out　that　the　controlling　capability　of　the　parameters　involved　in　functions　to　the　peak　position　of　the　envelope　with　single　peak　and　the　shape　of　the　envelope　are　essential　besides　simplicity　of　the　formula　of　envelope　function.　With　the　aid　of　the　method　for　determining　damping　ratio　in　structural　dynamic　experiment　the　so　called　stationarity　index　is　used　to　estimate　the　gentleness　of　the　peak＇s　slope.　By　means　of　this　index　this　paper　analyzes　the　gentleness　of　the　peak＇s　slope　for　the　four　normally　used　envelope　functions　and　some　of　them　have　been　modified.　It　is　also　pointed　out　that　if　Kanai　power　spectrum　and　Penzien　power　spectrum　are　regarded　as　envelope　function　in　time　domain,　these　models　are　powerful　and　easy　from　viewpoint　on　controlling　envelope　shape　ability.　Penzien　power　spectrum　is　even　able　to　describe　the　envelope　with　two　peaks　like　camel.　The　results　of　comparative　analyses　in　this　paper　can　be　used　to　select　and　simulate　earthquake　ground　motion　envelopes.