The paper deals with the analysis of residual stress and strain fields in a riveted joint. This stage of study concerns improving of the fatigue performance of riveted joints in an airframe. Riveting, particularly in aviation, is a traditional but still commonly used method of joining sheet metal components. Aircraft structures are thin-walled ones, with coverings made of thin sheets stiffened by stringers, frames or ribs. Sheets are typically assembled by multiple rivet or bolt joints. Rivets and bolts are also used to joint sheets and stiffeners. Therefore, fatigue resistance of the aircraft structure depends on tens of thousands or even hundreds of thousands rivet joints, which are used to build it. The local numerical models of the joint are considered with regard to the aim introduced in the paper. Numerical FE simulations of upsetting process are carried out using the MARC code. Three-dimensional numerical models are used to determine the resulting stress and strain fields at the mushroom rivet and around the hole. This type of problem requires the use of contact between the elements assembled and non-linear geometric and elasto-plastic multilinear material models to simulate the behaviour of the rivet and sheets. The influence of the squeezing force on strain and stress states is studied. A certain solution to the problem connected with non-uniform stress distribution in the rivet hole is proposed and analysed.