The work shows a summary of the most significant shells foundations built in Cuba in the last decades and the developments related to these in term of methods of calculation of plates and shells of complex geometry using reference surfaces and reference bodies, from the generalization of the projected solicitations method (Pücher, 1934) with the use of referential surfaces (Hernández, 1970) and other developments made in the mechanics of deformable solid by the Method of Duality (Rianitsiyn, 1974; Castañeda, 1993) and the Static-Geometric Analogy in the mechanics of the deformable solid (Castañeda, 1985).It also includes a summary of the research developed in recent years on the stress-strain states of soil under and inside shell foundations for chimneys of 74.5 m in sugar industries (Cobelo, 2004), comparative studies made of these with the use of the FEM (González, 2010) and other research projects currently running (Álvarez, 2010 ).