Around the world, a large percentage of buildings in regions of high seismicity are older, non-ductile reinforced concrete. To assess the risk posed by these buildings, fragility functions are required to define the likelihood that these buildings will sustain damage and collapse under earthquake loading. This paper presents the initial phase of a research effort to develop fragility functions for non-ductile concrete frames using numerical simulation; the research presented in this paper focuses on development of the numerical model and application of the model to develop fragility functions for a prototype non-ductile concrete frame. To enable numerical simulation of concrete frame buildings, response models for beam–column joints and columns are developed to provide (1) appropriate simulation of component response and, thereby, reliable assessment of risk and (2) computational efficiency and robustness. These new models are developed using existing experimental data, build on response models proposed by others, and employ component and material models available in the OpenSees analysis platform (http://opensees.berkeley.edu). A new beam–column joint model combines a new expression for joint strength and newly developed cyclic response parameters; a new column response model includes a new shear-strength model and newly developed cyclic response parameters. Numerical models of a prototype non-ductile concrete frame are developed that include simulation of one or more of the following characteristics: (1) rigid beam–column joint, (2) nonlinear joint shear response, (3) nonlinear joint shear and bond–slip response, and (4) column shear failure. Dynamic analyses are performed using these frame models and a suite of ground motions; analysis results are used to develop fragility curves. Fragility curves quantify the vulnerability of the frame and provide understanding of the impact of different component failure mechanisms on frame vulnerability.