Cities in South Asia are experiencing storm water drainage problems due to a combination of urban sprawl, structural, hydrological, socioeconomic and climatic factors. The frequency of short duration, high-intensity rainfall is expected to increase in the future due to climate change. Given the limited capacity of drainage systems in South Asian cities, urban flooding and waterlogging is expected to intensify. The problem gets worse when low-lying areas are filled up for infrastructure development due to unplanned urban growth, reducing permeable areas. Additionally, solid waste, when dumped in canals and open spaces, blocks urban drainage systems and worsens urban flooding and waterlogging. Using hydraulic models for two South Asian cities, Sylhet (in Bangladesh) and Bharatpur (in Nepal), we find that 22.3% of the land area in Sylhet and 12.7% in Bharatpur is under flooding risk, under the current scenario. The flood risk area can be reduced to 3.6% in Sylhet and 5.5% in Bharatpur with structural interventions in the drainage system. However, the area under flood risk could increase to 18.5% in Sylhet and 7.6% in Bharatpur in five years if the cities' solid waste is not managed properly, suggesting that the structural solution alone, without proper solid waste management, is almost ineffective in reducing the long-term flooding risk in these cities.