Increased impervious area associated with urbanization increases surface runoff. Thus measuring surface runoff and overland flow response to changing impervious area is important for stormwater management. We built an efficient lumped model to calculate runoff and overland flow for a city using a system dynamics software STELLA©. The model considers landuse and soil storage capability to estimate existing drainage capability and simulates for storm events to predict resulting stormwater volume in a catchment. We applied the model for Pullman, a small city of eastern Washington. To observe runoff response to urbanization we increased the total impervious area of the city by around 30% where area of high density housing has been changed from 8% to 20% and low density housing from 23% to 30%. These impervious areas have been accommodated by decreasing the agricultural land from 20% to 10%, parks from 2% to 1%, fellow land from 4.64% to 2.64% and public space from 34% to 23%. Our results show higher percentage of impervious areas not only increase the runoff amount but also shift the runoff pattern of a particular city. There is on an average 38% increase in monthly runoff, 2% decrease in monthly shallow infiltration and 13% decrease in monthly deep infiltration for various storm events. This urbanization results in 52.74% increase in drainage water. Projected precipitation for 2050s from different climate models results up to 69% increase in monthly drainage water. The model can be a useful preliminary decision making tool for stormwater management for an urban area.