The design provisions for semi-rigid steel frames have been incorporated in codes of practice for steel structures. In order to do the same, it is necessary to know the experimental moment-relative rotation (M-${ heta}_r$) behaviour of beam-to-column connections. In spite of numerous publications and collection of several connection databases, there is no unified approach for the semi-rigid design of steel frames. Amongst the many connection models available, the Frye-Morris polynomial model, with its limitations reported in the literature, is simple to adopt at least for the linear design space. However this model requires more number of connection tests and regression analyses to make it a realistic prediction model. In this paper, 3D nonlinear finite element (FE) analysis of beam-column connection specimens, carried out using ABAQUS software, for evaluating the M-${ heta}_r$ behaviour of semi-rigid top and seat-angle (TSA) bolted connections are described. The finite element model is validated against experimental behaviour of the same connection with regard to their moment-rotation behaviour, stress distribution and mode of failure of the connections. The calibrated FE model is used to evaluate the performance of the Frye-Morris polynomial model. The results of the numerical parametric studies carried out using the validated FE model have been used in proposing modifications to the Frye-Morris model for TSA connection in terms of the powers of the size parameters.