In this document, the comparison, with the aid of the three-dimensional finite element method, of the long-term behavior of a tunnel-shaft connection is made from two hypotheses; the first considering the rigid connection as a monolithic concrete structure between the shaft wall and the tunnel body, and the second considering a material of elastic behavior between the two structures, resulting in a flexible connection. The linear elastic material considered was neoprene, widely used in the construction of this type of structure. The geotechnical model used, the initial piezometric conditions and the proposed piezometric conditions to evaluate the long-term condition, as well as a summary of the tunnel and shaft characteristics and dimensions are presented. The Soft Soil Model was used to carry out the analyzes with finite element for the compressible strata. In the results analysis, emphasis on the relative deformations and stresses concentration in the elements of the connection for each hypothesis is placed. Finally, some advantages and disadvantages of each connection alternative are discussed to face the effect of subsidence in Mexico City are discussed.