Urban residents are often confronted with transportation predicaments. The inconvenience caused by the conventional fixed-route bus system has led to excessive reliance on private cars, worsening traffic congestion and air pollution. However, a flexible bus route can provide passengers with a convenient, expedient, cost-effective commuting option. This thesis studies a flexible bus system with Many-to-One (M-1) and Many-to-Many (M-M) demand patterns, comprising multiple rectangular residential zones and a central terminal. The total cost of flexible route bus service is modeled and modified for coordinated and uncoordinated headway conditions. Among them, the demand between each service zone and the central terminal, and the demand among service zones are analyzed to optimize headways in order to minimize total system cost. Finally, the sensitivity analyses are conducted to explore the impact of parameter changes on the results. The comparison of baseline and sensitivity analysis results shows that more benefits can be achieved when coordinating headways under low-demand conditions.