Instead of building new substations or transmission lines, proper installation of flexible AC transmission systems (FACTS) devices can make the transmission networks accommodate more power transfers with less expansion cost. In this paper, the problem to maximize power system loadability by optimally installing two types of FACTS devices, namely static var compensator (SVC) and thyristor controlled series compensator (TCSC), is formulated as a mixed discrete-continuous nonlinear optimization problem (MDCP). To reduce the complexity of the problem, the locations suitable for SVC and TCSC installations are first investigated with tangent vector technique and real power flow performance index (PI) sensitivity factor and, with the specified locations for SVC and TCSC installations, a set of schemes is formed. For each scheme with the specific locations for SVC and TCSC installations, the MDCP is reduced to a continuous nonlinear optimization problem and the computing efficiency can be largely improved. Finally, to cope with the technical and economic concerns simultaneously, the scheme with the biggest utilization index value is recommended. The IEEE-14 bus system and a practical power system are used to validate the proposed method.