In order to facilitate the precise transmission design of the modified gear,the maximum contact stress of the involute cylindrical spur modified gear transmission was calculated based on Hertz formula,the position of the maximum contact stress was analyzed,and the ratio function (called the stress ratio) of maximum contact stress to the contact stress at gear node engagement was deduced,and maximum contact stress was expressed as the product of the stress ratio and the node stress.The rule of the stress ratio of modified gear varying with both the teeth number of small gear and the transmission ratio was analyzed.The results indicate that when the teeth number of small gear Z1 exceeds 17,the stress ratio decreases as Z1 increasing; and while Z1 is less than 17,it increases as Z1 increasing; with the transmission ratio u increasing,the stress ratio increases.The stress ratio arrives the maximum for Z1 being equal to 17.If the design criterion of the gear contact strength is that the maximum contact stress is 8% more than node contact stress,the accurate design is required according to the maximum contact stress.The ranges of both teeth number and transmission ratio are obtained for being required in precise contact strength calculations.The formula of the stress ratio is verified by the example analysis with the finite element method.