Steel frameworks are widely used construction of multistory buildings for different purposes. In the practical framework calculations, the girder-column joint connections are taken as either absolutely rigid or hinged ones. The analysis of the actual behaviour of the frame joint connections shows that they normally occupy an intermediate position in the joints classification into "rigid" and "hinged" ones, i.e. they have certain pliability. Such pliability is characterized by different grades of stiffness that depends on a specific design solution of a joint. Therefore, to avoid possible material errors, the statistical calculations of frames should consider layouts with the joints that are able to support the corresponding amount of bending moments. This article contains the results of experimental and theoretical research of the actual behaviour of the girder-column connection semi-rigid joints using ABAQUS 6.13 computing complex, which enables us to solve problems by the finite elements method with due regard to the geometrical and physical nonlinearity. We consider the design of a beam-to-column connection with connecting elements in the form of paired vertical angles bolted to the beam wall and to the column flange. Based on the comparative analysis of the results of the numerical analysis and on the experimental data, the actual behaviour of the structure has been found and the stiffness of the joint type to be considered has been determined.