The downtown area in Yangon city, Myanmar, frequently experiences heavy traffic; one of the reasons is rampant illegal parking of cars on the streets. It has been pointed out in several studies that this area would be severely affected when a disaster occurs, and hence it is essential to clarify the effect of such undesirable parking behavior on the reduction in capacity of the Yangon road network. The purpose of this research is to illustrate the unfavorable traffic conditions that would result from on-street parking in downtown Yangon. We studied the mathematical relationship between travel distance and flow volume, and clarified the following mechanism. (i) On-street parking reduces the speed of vehicles on the streets. (ii) The unbalance of speed causes deviation of the shortest-time route from the shortest-distance route. (iii) An increase in total travel distance results in an increase in flow volume. We have also presented numerical results based on the detailed GIS data for downtown Yangon, and examined two scenarios that describe both evacuation and normal-life situations.