Continuous media theory in physics uses the Von Karman's theory to describe the shape, strains and stresses of thin plates, non Euclidian thin shells or surfaces. Given a set of boundary conditions, it relates geometrical shape parameters such as the Gaussian and the mean curvatures, the physical properties of the materials such as the Young's modulus and Poisson's ratio to the bending (or flexural slip) and stretching (or pure shearing) energy terms. Layered geological structures, especially reservoir bearing structures, have typically larger lateral extents compared to their thickness, and can be considered in a first approximation as thin plates regarding their mechanical behavior. Moreover, during sedimentation the top of the sedimentary pile can be generally considered as smooth developable surfaces in the depositional space, which are then deformed during their burial history under tectonic events. This idea is used to suggest a method for identifying the probability of finding sub-seismic faults in thin geological structures or reservoirs. This paper presents theoretical results that relate the curvatures of the top or bottom surfaces of geological structures and reservoirs. Bending and stretching energy terms are used as structural attributes to predict fracturing or the deformation style.