AbstractIn the direct boundary element method (DBEM) of analysis, much of the numerical computation involves the integrations along a boundary. The integration is usually performed by quadrature, and in recent pevious papers by the authors1,2it has been shown that integration can in general be carried out analytically, with the results of the integration presented as algebraic functions, and programmed accordingly. These results have, to this time, been presented for straight boundaries, with application to thinplate bending analysis only.For an arbitrary shaped curved element, the derivation of closed‐form expressions for boundary integrations is not possible. A semi‐analytical‐numerical procedure, based on representing the boundary as piecewise straight is developed in this paper. In this procedure, the boundary shape is considered dependent of the approximation of the boundary variables, and in the sense that each‘quadratic’ boundary element is considered geometrically to be made up of several piecewise cubic functions, the mulation might be termed‘super‐parametric’. Generally, a curved boundary does not necessarily imply need for higher‐order approximation of boundary variables, but does necessitate that the more applicated shape be accurately modelled.The integration procedure presented in this paper can be applied in other two‐d