Under the action of the physiological intraocular pressure the human cornea is stressed and reaches a deformed quasi-spherical configuration. If the deformed configuration is known, and the cornea is regarded as a membrane disregarding flexural behaviors, with the static analysis only is possible to estimate the distribution of the average stress across the thickness. In the cornea, the action of the intraocular pressure is supported by collagen fibrils, immersed into an elastin-proteoglycan matrix and organized in a very precise architecture to provide the necessary confinement and transparency to the light. With the goal of understanding the static consequences of shape modifications due to pathological dilatation (ectasia), we present a simplified stress analysis of the human cornea modelled as a membrane. A numerical investigation over 40 patient specific corneas (20 normal, 20 ectatic) is carried out to establish the relationship between the physiological geometry and distribution of the stresses, and to assess the possibility to obtain information on the stress state based only on topographic images. Comparative analyses reveal that, with respect to the normal corneas, in ectatic corneas the pattern of the principal stress lines is modified markedly showing a deviation from the principal orientation of the collagen fibrils. The rotation of the principal stress with respect to the fibril orientation is responsible of the transmission of a large amount of shear stresses onto the elastin-proteoglycan matrix. The anomalous loading of the matrix could be correlated to the evolution of time dependent shape modifications leading to ectasia.