Riveted joints have different failure mechanisms, some associated to the failure of the rivet itself, and others associated to the materials to be joined. The failures associated to the material are mainly due to the stress concentrations at the rivet holes. In joints with metallic (ductile) materials, these stress concentrations might not play a relevant role in the failure initiation, but with unidirectional composite (brittle) materials, they do control the failure. Both the orthotropic behavior of joined materials and the non-linear contact conditions between the rivet and the hole, make that the problem does not have a general solution. In the present work, several finite element analyses have been carried out for basic load cases, different materials, and orientations of the fiber. Furthermore, a two-steps least squares adjustment has been performed to obtain a polynomial expression of the stress distributions for all cases. As a result, a tool is provided, allowing the users to easily estimate the stress distribution (σrr, σθθ) along the hole contour, and σxy along the tangential lines to the hole circumference. Such stress ditribution can be used for failure predictions. All input and output data are available to readers, by means of a spreadsheet, to estimate mentioned stress distributions.