Cough is one of the early symptoms of the respiratory tract infections. Cough sound may indicate the physiology of respiratory tract impairment due to the infections. Inflammation, obstruction and excessive mucus may generate specific types of cough sound. In pediatric population, their cough sound may relate to the etiology of the respiratory diseases. Therefore, cough sound is very useful to support the diagnosis. In the physical examination, physicians may assess cough by listening to several episode of cough sounds. This process is similar to the way human recognize speeches. In this paper we present our work on the development of cough model using a Hidden Markov Model (HMM). The data for this work were collected from pediatric population diagnosed as pneumonia and asthma. Our developed model achieved the accuracy of 82.7% and 52.6% for pneumonia and asthma, respectively. It shows that HMM can be used to model different types of cough from respiratory diseases.