Normally the social approaches addressed in public housing policies are unclear in the implementation processes. Indeed, public agencies do not have systems that integrate clear social criteria to consider the social assessment of public housing projects. Therefore, the inclusion of social sustainability in planning and early decision-making is limited. In addition, social development technically involves variables that are not normally independent, and its completeness means their relationships must be considered to sum up the impacts. Thus, this work proposes a structural model that explains an integral interrelation of social criteria that determines socially sustainable housing projects for the vulnerable population in Chile. For this, a theoretical model was constructed and validated using a structural equation model (SEM). This system derives from the application of a survey applied to 188 professionals related to the development of public housing. From this, a model of social sustainability of public housing is validated with ten social criteria and eleven unidirectional interrelations, structured in two dimensions: the functional conditions of the home and the environmental conditions of the house. In the first dimension, the relation between the Improvement in family economic availability and Spaces for family development stands out. In the second, the strongest link is between Community health and safety and the Integration of the design in the context.