The application of mathematical models of rainfall is crucial in order to have a better understanding in terms of rainfall characteristics. The rainfall models have been used widely to improve water management, to construct hydrological structures and as an input in climatological studies. In this study, the gamma distribution is used to fit the marginals of monthly rainfall data. The parameters of the gamma distribution, shape and scale, are estimated using the maximum likelihood estimation method. Then, the sum of monthly rainfall amounts is modelled using the McKay distribution for independent gamma variables. To illustrate the independent example, rainfall data is used between the months in monsoon season for Kuantan station. The fit between the observed and generated rainfall data is assessed using Kolmogorov-Smirnov goodness of fit test. The results show that the McKay distribution is suitable to model the sum of monthly rainfall amounts for two independent gamma variables. The model is also useful for generating synthetic rainfall amounts for independent months in simulation studies.