The essence of this two-part paper is the analytical, aerodynamic modelling of insect-like flapping wings in the hover for micro-air-vehicle applications. A key feature of such flapping-wing flows is their unsteadiness and the formation of a leading-edge vortex in addition to the conventional wake shed from the trailing edge. What ensues is a complex interaction between the shed wakes, which, in part, determines the forces and moments on the wing. In an attempt to describe such a flow, two novel coupled, non-linear, wake integral equations were developed in the first part of the paper. The governing equations derived were exact, but did not have a closed analytical form. Solutions were, therefore, to be found by numerical methods and implemented in Fortran. This is the theme of the second part of the paper. The problem is implemented by means of vortex methods, whereby discrete point vortices are used to represent the wing and its wake. A number of numerical experiments are run to determine the best values for numerical parameters. The calculation is performed using a time-marching algorithm and the evolution of the wakes is tracked. In this way, both flow field and force data are generated. The model is then validated against existing experimental data and very good agreement is found both in terms of flow field representation and force prediction. The temporal accuracy of the simulations is also noteworthy, implying that the underlying flow features are well captured, especially the unsteadiness. The model also shows the similarity between two-dimensional and three-dimensional flows for insect-like flapping wings at low Reynolds numbers of the order of Re ε 200.