We address rapid transit network design problems characterized by uncertainty in the input data. Network design has a determinant impact on the future eective- ness of the system. Design decisions are made with a great degree of uncertainty about the conditions under which the system will be required to operate. The de- mand is one of the main parameters which determines design decisions. We present two uncertainty rapid transit network model approaches to study the impact that the estimation of the future demand will have in the design of new rapid transit networks. Considering that the new topology is oriented to dene public lines, to cover the demand by public transportation, a bounded budget and the modal com- petition between the old transportation system and the new rapid transit network will be included. Computational experiments are developed for these uncertainty approaches studying dierent network size problems under the main parameters of the model.