Engineers are tasked with the challenging task of evaluating the performance and analyzing the risk of systems in the context of performance-based seismic design. All sources of random uncertainty must be taken into account during the design phase in order to complete this assignment. The performance limit states for a structure must be defined using appropriate procedures that take into consideration the system characteristics describing the structure, the soil, and the loads applied to the structural reactions. This work aims to study the seismic behavior of reinforced concrete structures and provide new tools to deal with seismic problems, oriented to the new philosophy of structure design: the design based on a probabilistic approach as a tool to assess the seismic vulnerability that allows to define the levels of performance of existing buildings during an earthquake; it allows to build the fragility curves that constitute fundamental information and data in the determination of the degree of damage and to take a decision on a possible rehabilitation or elimination, depending on the level of damage. The seismic vulnerability of buildings can be assessed by determining vulnerability curves, which are useful for calculating the financial and physical damage caused to buildings by earthquakes. In this study, analytical vulnerability curves for low-rise reinforced concrete residential structure were developed, taking into account the structural characteristics. The probabilistic approach combines nonlinear static analysis (pushover) and response spectrum analysis to generate analytical vulnerability curves.