Covering a cough can be useful in reducing the transmission of airborne infectious diseases. However, no simple method is available in the literature for predicting the exhaled airflow from a cough with the mouth covered. This investigation used smoke to visualize the airflow exhaled by 16 human subjects. Their mouths were covered by a tissue, a cupped hand, a fist, and an elbow with and without a sleeve. This study then developed simplified models for predicting the airflow on the basis of the smoke visualization data. In addition, this investigation performed numerical simulations to assess the influence of mouth coverings on the receptor's exposure to exhaled particles. It was found that covering a cough with a tissue, a cupped hand, or an elbow can significantly reduce the horizontal velocity and cause the particles to move upward with the thermal plumes generated by a human body. In contrast with an uncovered cough, a covered cough or a cough with the head turned away may prevent direct exposure.