Traffic congestion has been one of the leading issues around the world. The emerging concept urban air mobility (UAM) is expected to provide a new solution by making use of the three-dimensional airspace to transport passengers and goods in urban areas. UAM application is based on a new type of electric aircraft that is enabled to take off and land vertically (eVTOL) and embedded with advanced autonomous and distributed propulsion technology. Compared to traditional aircraft like helicopters, eVTOL will provide safer, more efficient, and quieter air transportation service in urban areas. One of the greatest identified challenges for UAM application is to build well-distributed infrastructures to support eVTOL aircraft operations. Those infrastructures are vertiports (or skyports), where eVTOL aircrafts takeoff and land, onboard or disembark passengers, and get charged. On the one hand, dense land use in urban areas, aircraft operation requirements and community acceptance among many other factors severely restrict the number of vertiports and make it impossible to provide door-to-door (DtD) services through pure air transportation. On the other hand, vertiport locations should be carefully selected with consideration of its impact on potential UAM demand and system performance. In this project, we plan to develop mathematical models to design operation network for on-demand UAM service. Specifically, we solve the problem of vertiport optimal location identification and user allocation to vertiports with consideration of interactions between vertiport locations and potential UAM travel demand. We will also incorporate performance uncertainty of transportation network into consideration and extend the static model to stochastic programming. A case study based on the Tampa Bay area will be conducted to demonstrate the effectiveness of the proposed models.