A mathematical model, which can be used for the study of an influenza epidemic, was derived. The model of influenza takes into full consideration the incubation period and inapparent infection. That was analysed by means of digital computer under the conditions of changing the infection rate, .betha., from 4 to 5, for three types of communities (First type: the initial distribution of population, x$_{1}$(0)=89% susceptibles, x$_{2}$(0)=3% incubatives, x$_{3}$(0)=0.5% carriers, x$_{4}$(0)=7.5% immunes; Second type: x$_{1}$(0)=79%, x$_{2}$(0)=3%, x$_{3}$(0)=0.5%, x$_{4}$(0)=17.5%; Third type: x$_{1}$(0)=69%, x$_{2}$(0)=3%, x$_{3}$(0)=0.5%, x$_{4}$(0)=27.5%, considering the rate of population increase, in Seoul. In conclusion, the outcomes of this study are summarized as follow. 1) The new model is quite reasonable in representing many phenomena connected with influenza spread. 2) The more influenza does prevail, the smaller the valve of attack rate becomes, while the contagious period becomes slightly longer. 3) The average infection rate, .betha., of influenza is approximately 5 per week time and X$_{4}$(0) is about 27.5 percent of the total population in Seoul spring 1961. 4) The number of carriers of influenza in Seoul spring 1961 becomes maximum within approximately 2.4 weeks after the attack of diseases. 5) About 68 percent of all cases in the contagious period is infected with influenza from 5 to 15 days after the attack of diseases. The auther believes that the method to study the influenza models in this paper will be helpful to study the characteristics of other epidemics. It will also contribute to public healthe management and the preventive policy decision against epidemics.