This article presents a study on the structural behavior of the Government Building that is part of the old Lecumberri Palace and which currently houses the Mexican General Archive of the Nation. This building was inaugurated in 1900 and closed in 1976, after serving as a prison for 76 years. It was reopened in 1982 after it had undergone several remodeling works. The construction is made of brick masonry with lime mortar. It is supported by a deposit of overly compressible high-plasticity clays. The main problems of this building are the appearance of cracks in both interior and exterior walls, and moisture in the ground floor, caused by differential settlements. The study entailed a geometric and a damage survey as well as ambient vibration tests in order to determine the dynamic properties of the construction. The data obtained was used for the making of a model that, using the finite element method, was analyzed under different load conditions. This study has focused on the overall response with the assumption of smeared crack damage. According to the results, the building's safety was deemed as acceptable. It has the capability to withstand seismic actions as established by the Mexican Building Code due to the high density of its walls and the resulting stiffness, which infer that the fundamental vibration period of the building would be distant from the predominant vibration period of the soil. This highlights the idea that the building's critical condition is constituted by the differential settlements, which cause damage in the construction.