Hand, foot, and mouth disease (HFMD) has spread widely in a continuing endemic in Thailand. There are no specific vaccines or antiviral treatments available that specifically target HFMD. Indirect transmission via free-living viruses from the environment may influence HFMD infections because the virus can survive for long periods in the environment. In this study, a new mathematical model is proposed to investigate the effect of indirect transmission from contaminated environments and the impact of asymptomatic individuals. By fitting our model to reported data on hospitalized individuals of HFMD endemic in Bangkok, Thailand, 2016, the basic reproduction number was estimated as 1.441, which suggests that the disease will remain under current conditions. Numerical simulations show that the direct transmission from asymptomatic individuals and indirect transmission via free-living viruses are important factors which contribute to new HFMD infections. Sensitivity analysis indicates that the basic reproduction number is sensitive to the transmission rate of asymptomatic and symptomatic subgroups and indirect transmission. Our findings suggest that cleaning the environment frequently and healthcare precautions which include the reduction of direct transmission rates should be promoted as effective control strategies for preventing the HFMD spread.