Abstract Purpose – This paper aims to develop a new isogeometric boundary element formulation based on nonuniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach – The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique. Findings – Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation. Originality/value – This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.