A novel finite volume (FV) based discretization method for determining displacement, strain and stress distributions in loaded two dimensional structures with complex geometries is presented. The method incorporates rotation variables in addition to the displacement degrees of freedom employed in earlier FV based structural analysis procedures and conventional displacement based finite element (FE) formulations. The method is used to predict the displacement fields in a number of test cases for which solutions are already available. The effect of mesh refinement upon the accuracy of the solutions predicted by the method is assessed. The results of this assessment indicate that the new method is more accurate than previous FV procedures incorporating displacement variables only, particularly in cases where bending is the predominant mode of deformation, and therefore the new method represents a significant advance in the development of this type of discretization procedure. Interestingly, the results of the accuracy assessment exercise also indicate that the new FV procedure is also more accurate than the equivalent FE formulation incorporating displacement and rotational degrees of freedom.