This paper reports a numerical study on the local web buckling strength and behaviour of single-coped beam with slender web (SCBSW). First, finite element (FE) models of SCBSW connections were developed, and the effectiveness of the modelling techniques was validated by the results of full-scale SCBSW connection tests conducted by the authors and those in the literature. Subsequently, an extensive parametric investigation covering a wide range of web slenderness ratio, cope geometries and rotational stiffness of the connection was conducted. A database of the FE results of 243 SCBSW models connected with a rotationally rigid support was developed. The analysis results show that all of the models were governed by local web buckling, and postbuckling behaviour of the SCBSW connections was confirmed. The interaction among the slender web, cope configurations and rotational stiffness of the connections on the structural behaviour and local web bucking capacity of SCBSW connections was characterised. A practical approach for evaluating the local web buckling strength of end-plate type SCBSW connecting with a rotationally rigid support was developed using the available FE results. The post-buckling behaviour and the interactive effect among the slender web and the other essential factors were considered in the proposed method. The proposed method produces reasonable predictions of the local web buckling strength of SCBSW connections with a rotationally rigid support comparing with those predicted by the FE results and the available test data, which may offer a basis for a full-fledged design guide for SCBSW.